{ "cells": [ { "cell_type": "markdown", "id": "740862d3-1c9c-4e01-867e-8192d7f772af", "metadata": {}, "source": [ "# Statistical process of experimental measurements\n", "\n", "## 1. Description of the data\n", "In our lab some measurements of local velocity were made with a CTA probe (see for example the [Wikipedia page for hot-wire anemometry](https://en.wikipedia.org/wiki/Anemometer#Hot-wire_anemometers), or the [Dantec information](https://www.dantecdynamics.com/solutions-applications/solutions/fluid-mechanics/constant-temperature-anemometry-cta/measurement-principles-of-cta/))\n", "\n", "The measurements were performed in the wake behind a NACA profile with 5 degrees incidence angle\n", "\n", "![image.png](profileWake.png)\n", "\n", "The data provided have been acquired at a distance of, approximately, $\\frac{x}{c} \\approx 1.1$, where $c = 265 \\,\\text{mm}$ is the profile's chord. and there are 17 $y$ positions, \n", "from $y=-4 \\,\\text{cm}$ to $y=+4 \\,\\text{cm}$, in intervals of 5 mm. In each point the velocity has been acquired for a second with a frequency of 1 kHz (that is, 1000 velocities in each point). It has been measured only the $x$ component (main flow direction).\n", "\n", "Most of the topics covered in this notebook have been consulted in the [CFD-online Wiki page \"Introduction to turbulence\"](https://www.cfd-online.com/Wiki/Introduction_to_turbulence)" ] }, { "cell_type": "code", "execution_count": 1, "id": "alpine-convert", "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "import numpy as np" ] }, { "cell_type": "markdown", "id": "careful-behavior", "metadata": {}, "source": [ "We define the names for the columns, according with the definition" ] }, { "cell_type": "code", "execution_count": 2, "id": "judicial-somalia", "metadata": {}, "outputs": [], "source": [ "columns = []\n", "for i in range(17):\n", " y = (i-8)*5\n", " columns.append(\"y = \"+str(y)+\"mm\")" ] }, { "cell_type": "code", "execution_count": 3, "id": "ranking-times", "metadata": {}, "outputs": [], "source": [ "turbulenceData = pd.read_csv('TurbVel.csv',delimiter=',', index_col=0,names=columns)" ] }, { "cell_type": "code", "execution_count": 4, "id": "earned-stability", "metadata": {}, "outputs": [], "source": [ "turbulenceData.index.name=\"Time\"" ] }, { "cell_type": "code", "execution_count": 5, "id": "placed-lobby", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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y = -40mmy = -35mmy = -30mmy = -25mmy = -20mmy = -15mmy = -10mmy = -5mmy = 0mmy = 5mmy = 10mmy = 15mmy = 20mmy = 25mmy = 30mmy = 35mmy = 40mm
Time
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" ], "text/plain": [ " y = -40mm y = -35mm y = -30mm y = -25mm y = -20mm y = -15mm \\\n", "Time \n", "0.000 20.916005 21.013892 19.890369 20.564816 19.247617 20.242762 \n", "0.001 20.757920 21.124463 19.878740 20.528820 19.258909 20.278330 \n", "0.002 20.661140 21.087559 20.101135 20.492846 19.213710 20.337691 \n", "0.003 20.794288 21.099841 20.207287 20.421109 19.315560 20.219094 \n", "0.004 20.952667 21.099841 20.349604 20.480892 19.292888 20.313920 \n", "\n", " y = -10mm y = -5mm y = 0mm y = 5mm y = 10mm y = 15mm \\\n", "Time \n", "0.000 20.171834 19.326923 17.711748 17.954515 19.112384 19.247617 \n", "0.001 20.124676 19.417902 16.314876 17.534186 19.213710 19.292888 \n", "0.002 20.136438 19.360977 13.902128 18.590930 19.202443 19.349631 \n", "0.003 20.124676 19.349631 12.840679 18.340470 19.281544 19.372364 \n", "0.004 20.148242 19.326923 15.086783 18.243283 19.247617 19.349631 \n", "\n", " y = 20mm y = 25mm y = 30mm y = 35mm y = 40mm \n", "Time \n", "0.000 18.955669 19.624038 18.989162 20.337691 17.901476 \n", "0.001 18.922264 19.704760 18.833365 20.313920 17.743229 \n", "0.002 18.933382 19.716296 18.601871 20.254624 17.922668 \n", "0.003 18.955669 19.785785 18.503472 20.278330 17.471901 \n", "0.004 18.944540 19.785785 17.838033 20.195451 18.135857 " ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "turbulenceData.head()" ] }, { "cell_type": "markdown", "id": "married-obligation", "metadata": {}, "source": [ "If we want to save this data in another file, keeping the information for index, columns, etc... instead of csv, we can use a more powerful format, as HDF. This is a Hierarchical Data Format, widely used to store big amounts of data in a organized way. More information, in the [HDF group web page](https://www.hdfgroup.org/solutions/hdf5) or in [Wikipedia](https://en.wikipedia.org/wiki/Hierarchical_Data_Format)." ] }, { "cell_type": "markdown", "id": "9d6d24d4-1898-4a45-83cc-85f1133296c6", "metadata": {}, "source": [ ":::{warning}\n", "In ordert to save as HDF you will need the [pytables](https://www.pytables.org/index.html) module installed.\n", "\n", "Just run \n", "> pip install tables\n", "\n", ":::" ] }, { "cell_type": "code", "execution_count": 6, "id": "foster-happening", "metadata": {}, "outputs": [], "source": [ "turbulenceData.to_hdf(\"TurbVel.hdf\",\"w\")" ] }, { "cell_type": "markdown", "id": "faced-frame", "metadata": {}, "source": [ "We can then get again the data with the format provided" ] }, { "cell_type": "code", "execution_count": 7, "id": "imperial-actress", "metadata": {}, "outputs": [], "source": [ "newTurbulenceData = pd.read_hdf(\"TurbVel.hdf\")" ] }, { "cell_type": "code", "execution_count": 8, "id": "collected-mumbai", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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y = -40mmy = -35mmy = -30mmy = -25mmy = -20mmy = -15mmy = -10mmy = -5mmy = 0mmy = 5mmy = 10mmy = 15mmy = 20mmy = 25mmy = 30mmy = 35mmy = 40mm
Time
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......................................................
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1000 rows × 17 columns

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" ], "text/plain": [ " y = -40mm y = -35mm y = -30mm y = -25mm y = -20mm y = -15mm \\\n", "Time \n", "0.000 20.916005 21.013892 19.890369 20.564816 19.247617 20.242762 \n", "0.001 20.757920 21.124463 19.878740 20.528820 19.258909 20.278330 \n", "0.002 20.661140 21.087559 20.101135 20.492846 19.213710 20.337691 \n", "0.003 20.794288 21.099841 20.207287 20.421109 19.315560 20.219094 \n", "0.004 20.952667 21.099841 20.349604 20.480892 19.292888 20.313920 \n", "... ... ... ... ... ... ... \n", "0.995 21.087559 21.248015 19.349631 20.007225 19.785785 19.832212 \n", "0.996 21.013892 21.334855 19.474945 19.972095 19.774176 19.855463 \n", "0.997 21.050677 21.310005 19.440708 20.054129 19.704760 19.867080 \n", "0.998 21.001619 21.297609 19.452103 20.054129 19.727874 19.832212 \n", "0.999 21.062977 21.272798 19.497812 20.112884 19.612552 19.855463 \n", "\n", " y = -10mm y = -5mm y = 0mm y = 5mm y = 10mm y = 15mm \\\n", "Time \n", "0.000 20.171834 19.326923 17.711748 17.954515 19.112384 19.247617 \n", "0.001 20.124676 19.417902 16.314876 17.534186 19.213710 19.292888 \n", "0.002 20.136438 19.360977 13.902128 18.590930 19.202443 19.349631 \n", "0.003 20.124676 19.349631 12.840679 18.340470 19.281544 19.372364 \n", "0.004 20.148242 19.326923 15.086783 18.243283 19.247617 19.349631 \n", "... ... ... ... ... ... ... \n", "0.995 19.612552 18.844470 17.010890 18.877784 17.234927 19.937022 \n", "0.996 19.601036 18.844470 16.960352 18.082340 17.513403 20.183621 \n", "0.997 19.578058 18.888878 16.373577 18.623839 17.680285 19.960385 \n", "0.998 19.681671 18.933382 15.899636 18.039642 17.440815 19.693194 \n", "0.999 19.658606 19.045057 16.570464 17.173579 17.327294 19.532177 \n", "\n", " y = 20mm y = 25mm y = 30mm y = 35mm y = 40mm \n", "Time \n", "0.000 18.955669 19.624038 18.989162 20.337691 17.901476 \n", "0.001 18.922264 19.704760 18.833365 20.313920 17.743229 \n", "0.002 18.933382 19.716296 18.601871 20.254624 17.922668 \n", "0.003 18.955669 19.785785 18.503472 20.278330 17.471901 \n", "0.004 18.944540 19.785785 17.838033 20.195451 18.135857 \n", "... ... ... ... ... ... \n", "0.995 20.373413 18.800155 17.451182 18.922264 19.808986 \n", "0.996 20.148242 18.800155 17.440815 19.532177 20.207287 \n", "0.997 20.148242 18.329634 17.461523 19.797365 20.160017 \n", "0.998 20.709496 18.211012 17.607118 19.601036 20.183621 \n", "0.999 20.721574 18.050324 17.378822 19.486393 20.065853 \n", "\n", "[1000 rows x 17 columns]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "newTurbulenceData" ] }, { "cell_type": "code", "execution_count": 9, "id": "competent-chemical", "metadata": {}, "outputs": [], "source": [ "del(newTurbulenceData)" ] }, { "cell_type": "markdown", "id": "consecutive-atlantic", "metadata": {}, "source": [ "We can easily plot velocity time series in any point" ] }, { "cell_type": "code", "execution_count": 10, "id": "acquired-chapter", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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X8ytxiR1jKE9owZ8jttuCnzHL11reKv/kkk34xl0LQ70gRPxm3hJHMy6bDO1CWIT7Fq3FMVc/jP/+xxsAgAHbY2GgxJSCXxyA/OfX1+6IFNyz/+tRXCSlxuNgjDn0SRysEXaJistu2bPk9XU7nEnU2blb4Zglgo8/5u6BsqdN3DASccCbGyZYKy5bmvTX2N5QlVRlxJQQt33iSEwYZmnyfDIbP6wTBwucOwBcd/9iT/virNS4xi+3nxQaf3vBgGGQM3FMHtWNqaMHh5bfXzKxdMPOzL14vnbni7j4Zu9Y+cLtC/D3RWrKNUu0lOAvmww9l83BjYJGkyd29XFDLMOx18zF7J94uTweulje8h6Eq+55xVkalhlDm7RjcuWW3bjm7xanzLW+gbKpdH1UucTdPv9tfP3Ohb7jcXHLk8uwfFN8z6CNO1wPET4R3fT4W3h1zXZMHN6Fz59keYnc/MQyXGjbPfh5ccM4c4jCR6YRuOCXwwmnovHb//k7KBbSH4KyFs3tCZWgGCD5bxZ84QHvzvFeW1kY1F7EJcdN9Zz39NJNWCRk94rz3jrbCugtlQON06LGr9qQV4xBz13x10XKYG5p4ran38b9L1fvMJEGWkrw8y3h3MCWNzifywe97NvONaUhnW2xyxQ3MMlb5Tl29ZfQZwv+h15d5ySrVpVzw2Nv4S8LVjrHn4mZmlBlD5BzpUZhk+AayCeiK+wELv/6zsn4tOAe+PRbmzztro7j9wp4LsRkWqJUNrFi867QdI07+krouWyOhy4RweUSF85x5X5/ycSlty+IFYxPnp/4BFZJzgKRPly4cit6LpuDJ5dsxPfmvBJ4ze5+q691tReUtKbYjiC5Lza1s2gZd+WiegdMvL1pF/pLJnpGdeOmCw9XlhU0eYn4x2vrU/G2axS0mOC3fd4TRopMG1EiKkiG3f7Mct8xrsnLVI+Iu55f5bhubt09oAyaxZhVxnf/9rKTPAWwBOstTyxVUj7cCAqoA3GFGQZVEBN/cL6fu+R98ripyvKqDdLGmKvxF+3yXY3fSzHd+PhSvOs/5/pCBnjuwbbPyBqxDM4aye+6bFp2HlGL3dlXwpV/W4Q7n1+Ji29R02resr2F8vsQhekZB+8RWQ7gfYeP2zF+Hn51HU6ZOS7wGt5XOtsKvlUoALQX3TLjvLeONgN9JVOpzR97zVyYjGHiiC6cMGOs8vo4Gn+roaUEP+eKay34gygD3q9V2vO6bb346p/8ETg5D102/VQPR8GI9lgwGcNvH/drqSs278Y3/7II192/2PfbJb93A3ipdnjG0bTEe90mUBJcHmza2Y8TZ4xBsWA4gtlzPSoM2eDUwxxqghv5uLCT6a9fPRK935AbUPltPbJ4PX78gMtr89/5ZiG52XfMfxvfuGuhx2Pmy398Ab9/0pr0F6+NdjGUuWrVruArztg/shzAK/jF/jl5ZHfgNd84fT90FA0M7ig614tjTrznoB3X4pvuKBbQO2AG2kPKTG234qjeEyt/pOFRF4aWysDFDYJBlEiWeGqJm7h6Z0C0QpX2xxHkD8+1VZMFuxoueHtrZMwVBq/glRG1DN7ZV7aCcAhQCWoZQff4uduewz5jB2Nb7wCmjbWMcyqNr2xWJvj52Yy5LqcGucc8J1UAPiFd+NunYTLgo0dNwejBHY7wdPMIeCvhdNfW3QPY3juAtzbsxNNvJaMg5En+5dXb8Klbn8Powa57pcrjRgWP4BcmNdNk1sYqRb885/DJOOfwyQBcbXtYV5vjwz/g8d7y3v/4oZ1Ys63XMzm0FQilshmYV9lk4TRWIUIBIaq/HMxlk2W6UmkpjZ/70SdNClItFry9BecIQchUW9MBd0Aw6TsQHI+E2wXCNP7bnl4eKbiZ6cY+V7YtQrCqQurKsWKcuoTPIjcv0km9AyYWrtyGUpkpDaC8aMe4W+HILTPmeOtwwRYn8FtQAC+SJg9ehEy/8MvFdhvkTgQFInzi5vk44+eP+wLuRUHe93Db09ZqQaTwgvqKDJWWzWD1Rz6xf2TWnoHX81Vfl2D8FZ+r/N6+d9YBALx93zDI0upD3KDDdIw24ccHLz3O93t3zJDm/SUzceC26+e9iZ7L5kS67coKwK6BcmKHhSRoMcFvCaewTn/tfa/iN/PUG1MqheyXr9L412ztdQaEu8s2OmQs17hKIRx/HJiMhQa7ilp6qn7e3V/GkM4iJgobdnz1Cre1XbEqCdo0xTVR7vaZJFBX2WROwDJTiE3DtXReVBg9FhRxMmgCKjtUD+z2+qkeIvKEWwiarKPehSz4RYGfFOKkK84BZZOhYBBev+q9uPqDB4VcT57/gHrnNUd3hyWExXsoEME0g+mccshv8j2MtKN9ilCFllBh+jfujYz7L+NnD1nu1FFxoORXetAV9+Pa+7NzQmkpwc+5z407+3Dk9x/CFXcvwuK12/Hf/3jDCTb1i7lv4qp7gj0WKoFslJQ510cWr8eRP3jICaHgbLYSbAFBMW+4JmGyYK+eOGAI13CjNGrVz70DZQzuKPoElWejlvDbGkW2p1LZVNoK+EB3BGiE4L/hsbfwEdso+8dnXbc9k/mDc/H2hvl1B2lw/BkG0XacrjIDNH7+/Q9PLw/MlxBFa6W5A3VEt38VyB0BCgahzfabDwJfFbQZBn509sEAvP1abuqQDqs+cXIocI0/jOoJa4Mw6aiUI64Inn/UFFzzoeBJDABeSJiNizs9RIUuUb3ROzJ0L20pjt9NsGwJ+Zv+uRQ3/XMpAGDRym34xb+9I7W6bnlyGcYN6cCp+4/3CS7ZA4ZrdjwzFRdE4gCWfco5xA1ccZfvKpiMhQt+qd/KLo3yxHDaTx7Fy6u3YeLwLuc+zjpkD9y1YBW6291uJ9a5VhG62aJ6gl0CuRCJEobfFXKwbhE2zpkm8wlYfithAjQojHJQO+Tnx9+x+NiIyJl0Nu0M1tJLJkNYJsusNyIxMJQZi+TOAZc+aysSJo6wVn4l08Rv5i3BEXuN9E3Ygzr8N1YwCOVysFYfTfW47QyjeTsD3E8rgWky/PPNjc74DEs/CXBlw1t3lqHGW0rjD3uQQXHH735hlZK/DsOWXf345l0LcfEtz+L+RWt8m5hknlDeOcrjgosDeEdf+CacJ5dsqiq4Wn/JDF2Oim3Zsqvf59IoPtu+UtnZjFYwyKEzPnPiPth/j6GYMNyNHCoKynWKzFADpqk0ErtZxKx27egr4TO3PqfMESvvRRB7gTjhybH9wzKUBe1oDtpPIPc9lXHXoHj7Ec78+eM49Mr7A39PK8/C8O42z7MSjevlMou1B4HbT4qG65VVNhmuuucVnPmLx333qwpgWCBL4+fZuGREUT2iMFf1Jb6fpr1gxDKomibDtt7w8XjDY2/hPCHaayTHr6onQ4NzSwn+MK2wYJBPIC/buBOfv+15XHxzslgaorZ28S3P+hKhywJF1gZUVM+OAIOwiGqSQn/ol//Er0NsG6KGq+LixTtaI2juluC3fu1sK2D04A6Plie+k229Az4+3/JuUFA9ksvln59fiTkvrcaPFLyoJ9Jn2fRo2Sbza/ZhHP/MCUMBqDNCifcjC/pzrrcmSncDl7cuwFrFxBnsr63djs27ggVPGhr/vuOH4B2TRyiVJca4cTdafPBn31Yg103WE2TPW36HYiljGJbtY8ootQupGWL45XVzhKXafP/Be8TS+H/5yJs46Ir7HaP79+95Bdfe5w2zsmDFFs/3KMGves7auJsSwgS/QX6Bxge3nJw6ClHLOrkdcqe4+4VVOOfXT3jonR0xUuBFZUt6f8imnagMWWLHVIUA8MRfkeL+8O8dRUvrCzLubd094PH+AKxJUvTK4B+DqB5VIDIxNd+v5y3x1MkURm1u5FXZVc44ZA+7XeGCX8babX3KNH9iWwjpDPb+mIHxhoREiTXIepIeKkr43WQslpAca2vpx08f41CRIt8t3y+fS46cOtI5VjCs+oIWQ4yFu3MGhcW45Pi9ceMFs5zv7QF7RWT8+XlrZzvPZHb9vCX4xVzvHg85QU2QosDBmN8AXM1u9Ci0FMcfNusSkUdTmvGNe3HHJ4+qsJ7wlywH+1Kd/9Rbm3DHfNe4k0Z2qEkjgr1roiBr5jKCNuVwjwzA0uYs7U09STAGdLcXfXsOxIFbNAz0Cz7d/Fly4a0a/2J75HAd35vzCi48pseqX7oXlXDnE1OQgA8y7vLyHD/+AI0/jF6Ki7hlDB/U5gQOlGEY3ObgHhM3cJXMeIK/Z/QgPPbVE7HHsC68ZicYEWky+TkSEZ65/N2efQYFslbjQSuZMMMvELyf5JSZY3HYFHeCaS8agXYLUbHhtrgwO4z8m7hiLgc8u0t+72UWNMefAp5dthnf/MuiwN8N8nbCvpJZUb5RIHpZJ+/cjROaN2iAJkGSPAAyPAm4dyuoHuGWxPFZMAidtsbdViRrImAMc19bhyXrd/gGvsq1Thwk/HPBnkDijI2oAfTbx5c6nx9+dS2+eZcVmE4lQLngD3IfDVtVDpRNZ0XCtTlPOGxyA5zFQdCqIyrr2QETLbrqtxccjnOPmKQ0ePJomPKKhMOMKfgBYM8R3TAMcgSwRwhKj8sgYMyQDk/QN8MgbOst4R9iohaxLYyFRjkN4u272rzjob0YrPFvUVBrcnRdEZt3SYJfGOOyFxlg3cMTb26UjgUWXzVaRvA/9dbG0N8NIt+gXbm5sqQI0YJf0vgDBqroesapnpP2HYtLjvfGF3//wXvgfQdNiGxXd0x/ZRXEZ6NafZiBVA/htk8cia/MnoHu9qIjsC/87TM46UeP+IRyp2IzjcjRcmFDRErBp9b4Q24MXk+Pj9/kxsJRlc8nsUiNX2GuK5WZwPH7qZ5tvSX84Sl/PKYgBK0CRc34J/9yCOb+vxOc70dNHYW/fe5YAMA+Y4fgBx88SPnMt+waCNWiS2ZwCIUg8HcnCkHZ1VdF2UTVY5rh3H2QLUJWMiyNX13O2u1+KlSmYrbs6nfyVG/e6Z0URJmgCtmi0k2y5PhbiuoRcey00Vi5ZTeWrLd4ug07+nw5T5dtsn5L6uEVxfGLu2BNkwVOFKJA4oP8W++b6Us+XjTI4yIZhLQEv0ogigLMQ/UYwD5jB2OfsVZkTcPwGjBlzVnVRnHgOhp/gOCParsKQzrb0Lejz6cpq+weYRq/afo9hEQMeJLL2NdUMbZ39JWUWa76SyaOnTYa33zfTCfcBYdK+1W5AW/bPQACeTV+W7gyu/1JXR95PeL48FM9/uui6jGj3DkDNX5J8Idw/KpJVm77cdfMxbbeEpZefbqPlvIIfu4AINKc8Hv2ZEn1tIzgl5/h0M42YDgcwf/M0s14Zulmzzlr7fDFYdqECkE+3hyixj/16/cEumGKAm+77c7ZVjR8mopB5Au3cOenj8aQjiJOEfJ3xpkcgiD2caXA9VA9ooui9+YK5DVCy1qNPBgB78AtClRP3Pj4UQNItfQOwig73o1KG5v69XvQaedSUNVYKjOHLqk21AQQbMwfKJvoKBqYPs4NntRWsOwHKiGvEnb9ZROGIe8zsP5bG7jMxIKfn9/roXokwZ8g+xtHlKE5yLirEvxBuTB4qGm5XhFh8bBEO55l42jz3DtjTOHyG1hc1cgy2fqNRLSOiBYKxw4hoieJaAERzSeiI7KqP7p90edwv/KkXTGIuuHweZEEvGAxxSBPUtJeMPDhw/bELRcdga/MngHAGuiy//M7Jo/ANGHgA+rNMXHh1fgV2q4o+BVaIodhkMcrSB7485f5Y92LA9eleoIyYvnfluq0757pRqeM4sRF8N3RwbGT/BuzOCzjruvLbp0Yu2ofgjy9+kumb4cqf2cqIR80FmSNn8PawJVc4y8qqB6fV4+iyFWRHmdRVI/6t8527zMyDFLSXoCavg1bScrNEe+Zc/nemEWBRWWCLDn+mwDMlo5dA+A7jLFDAHzL/l4TxOm06+zNQEkTWPRGavzBb/lX570Dnz7B4vD7hfP4JDS4o4jOtgKOnTbGccfbPVCOFa6hOo0/AdUjcvzSeUWDPILW79rqL1u1ASdI44/y6uHYc2Q3Hv3KiQCit9Or2vIJKYWeCjJ/LU6YfMKrRuP/03MrlMf7y2bgLm7V8aD+TeSdl8SzqtH4uRC0QlREtyWqGiuOT/DvQYJfNWZUK05AbXQPdw/31skTBwHuysDz7lm+EUIzE/yMsXkAZPWNARhqfx4GYFVW9UchjmHKiYqYUOWPNO6GUAuzD5iA0w60DLUiJbR2Wy8MgkMlAMBg2+VtoGzG2nE4KCXBr9J2xSNRG+U85caQuSLV8+/HWqn8Rg5qj0X13Pb0cifvsKcdRM5O0CQhneP4eVtgvuBoJdN15+TvthpN77an1bFcBkpmoCIQ1k8+fNie+NxJbpYz2Z2TN54xS3lJKvi5Vs7zP3NDv/cc/3WRxl0Wf+euqj0iggK2qejbsElbbrO4F6gsJE/iUDkDZIm8vXq+AOBaInobwA8BfC3oRCK62KaD5q9fr3bjqgZhO/04+MCtxLgrCqv//NCBOHlfNztQlJ8178RyrJ5BHUVlZx3UUYwVp6c7JapHRY2Ig+CN9cHJQuQBGodfF20dH3/XXpg4vAuTRnQrqR756Xztzpfw5BJL/7joXXsJZVLildzE4V2xhd3u/jIOv+pBz7FS2XU75JNW2ga8Z5ZuwqqtvWgLiEmjDHhnHxozpMNROgBvmGjAfbYMVrvjT4JueYDrdWTYrr3ia1D176gnZEbQTnKZf/rUUfjG6fs538XosUEavypWVtkMjpQa9l5d4654fuDpmSBvwf8pAF9kjE0C8EUANwSdyBi7njE2izE2a8yYMVVXLL+gKC2imkiXuwfKHq5wvwlDPXx7VExv3on7pQlC5vF5GIehnW0xqZ7KBb/J3GdYUsTP4b9t3T2Ay/8cnKDdp/HLxj3Fa5H9zDuKhhUTPibVw7HX6EHOZ8OgRBrru/cbi9s/eWSga+A/pd3dOxWCwtp4Zk/qiiBtMg6eNDy0TaoQBmfbMZTk/sAnPZWHCzeoFog875UQLJDibuBS1cM3cBUMCqWlOKJWZKbJYtnsOA6bMtJZOQLAvV84Fo9fdhIAtTsxoA6lHhTKXLUbXISTPEgy7uaJvAX/+QDutD//H4DcjLvycw0LM/Ljcw72LPl6B0x89IanIgMzieeLHWhEd7vH2BYVO56PA5lLlzdgnXnIHpi9/3h88ZRpaBPymP7HydOU5ao4/v9OEJHU3dHqj5jJn+926RnJA1LWsuU50Np+7z3WIQ1GvrEoafhhcQIpGJRoJffvx07FniO6URDumw/W19dux7/+z1NBlzoold2YMnE0/r985pjA3w6cOEzpyskhT5ZcoKuoHv5K5MnQIFJSEGJY5iQgu0l8xVggy94TlRgpUvBHUD1RGNrZ5mj9QW1RJU8qm+o+GKW9ixF1OXJW+HMX/KsAHG9/PgnA6znXL4ACPQFGDurwabSPvr4B97y4Wnm+iJdXbcNtTy/3+P2OGNTu2WD18qptoWWoqB7Ar7EP7WzDrz56GMYO6XS0ponDu/DFU6YryxWv/79LjsKVZ+6fSPjxjjqg0NLESUGEXLwsLORBffz0Mb5z5MHIwxerJtAwd0BxMi4Ywe9fhfFDrYii4kqRUxaq2EUqlMqmb1KvlOrpai+Erhzl98MnHNWKhTehQNIqiLx0hHvrDNt7S8pImmHgl3NjumEQ+lIR/PGcNeQ9Dco22jf5jsnDPcdVGv9ra7Zj5rfu8x2Xx60q8CDgffc5K/yZunPeBuAJADOIaAURXQTgEwB+REQvAPg+gIuzql+G/FzDdsX5BoCNJRt2OoGZgnDLk0sBeDnBQe0FTB83xNlBuTEkxgcgZpfydqDOkCDsfECHDRJRGBzeMxIfO6onkfBzwxWrBL/1W1QI6yiq54dnH+xrk7z8trhnNWUWdjsewU+ud1Ac7GFrhOL5Ufs1ZHioHkfjT1SEg0HthVDjtuzOye9XRfXwd1As+DV+EWLO3a27BzAsJFWnCrw8R+M3uMYfTkFGrZBlO4EKj192Ev4csoIS8dhXT8QtF73T+d5WIKVda85LakVQHoPy/V33wGIMlE0pThXDuKHqsNNZILMNXIyxcwN+OiyrOpMgLPKdYai9N66ftwTXz1uCpVefHnjtuKFurPkPH7Yn/vjsCkeQxdWu3QFitXFwRxE7+kqBm0sAoN2meqIGyTUfOsjjmiY2afzQThy05zDcL+0M5nAEf8mfDpE/zihhGKXxd7cXfPYXWSPkRkExMFscjUn0iOLtMAiIEt/nHTnZEaRiv9jVX8ZwRaTg9oKhDChWKruxhZz8yhWqet3tRY9xu69U9qw85Im54FA9wRq/QeRZEVgcv2DcJff8SgQ/v97R+MnS+KNShqpWRUM6i0403ThUT1j6Txl7jvC+VIPUgj8I8hjsKBqQ0ya/sW6HJxAdg7WCHyiz0OBvaaFlYvXICNP4DSIPl5sE3EXw48fshR+efbBnkohyObvUpmhkjX+o3UHCNCM+0MsRXjIfOXwSPnZUj7JNHzl8Es4/usd/kY3X1mzH8dfOxStrtvkoAy7AZKOmrL3LQl0W/AWF0VVFBdy3aC2+ePsCAF5DZhh1IlM9QLw9Gl8/zfUAEftF0OoqKGl9yTQdV98gd86pYwbJlwEAfvOxWU7/ACwtVNT4P3Prczjiqoec7zI3L050MpwE74bX9mXI7pw2dvaXUDZZChq/FUK6EqqHG6u72goW1VNNFqIQdLcXUDTihwcBgB8/sNjzXXV/yzbu8tBojFnKaJBXUdpoasE/b/F6/PbxtwD4BUKYZlwwKNB7IwiMMdzz0mr02RuQLjl+asQVXjxx2Un4vG2UlTl+LkjCNH5X8CfTIL0D3UuVjBdWLwDws4ffwLKNu/Diiq1oLxq46cLDnd9MR+MPp3pkN1qV4JfHsGzc5c9HzJzEEUZ/iFSZLPgP7xmhvOaaDx3kMYqLGn/QJDOsS72QHigzhwLk8Zpkjf+de43EfV84zokT/1/nHIL3HTQBp8wch9MOHO+2o2B4qK4HX1nnKadbemaiVi+Dv4KCYXg1flLfI19ZJBX8HHw1VKhC4585YSguPKYHRYMiY/VUime/8W48+fWTHe+juODpXDnk/gtwjyC3zNfXbceS9Tur8rxLgqaO1fPAy2sx56XVuPCYvXwCIZTqCeD4w/D0W5vw6Vufc4RWWNYoFcTOz8ceb/PQTlvwhwyQSgW/aAw1iDyak9xc8Wt3ewEnzHD3JvQOlPH2pl2+nbc+466s8cdws/VRPdJjaCsagL2U7i+beHP9Duw9xm/IU1E9/H9HseBQaiI+fNie3vZ5BL+vCgDBAvGtDTuxcafV0IGSWuM3iDBj/BDMGG+5/5516EScdehEu263/W0F8gT7kzGrZ6TnOxeeKpsO/61A3vsjIqW3SaWCn1fdLxh343j1qLRgInIoP8aSx9OKg1GDrdU7t0VUCtX9lU3mmUw+esPTAII3kKWNptb4DUFjkTV802T4/En7eHg2joJBiTen8Pg8XI6pE4QHXy9yslz49Usaf5CPMRAdQyYIns0z8A98EeI99YyyKIkHL7WctL70fy/g2GvmRmpG8nzoz8Dkf0jyfcueO6K94c7nVuLkHz2C1+2kHyJEqow/Y36L7UVDaSCU2yNqxEGTbJBAvO6Bxc7E6GzikSe+sGBjntAVhtK4PXXMIOwxrBMHTBzmOc5rUVI9Qt3e9+9dkfC28tj0aRh342j8P/jggb5jBOte+HNMK0m6CgXD8O2pSYJAwa+YTDTVkwKI3OxPqmTXs3pG4qUr3uPZVQt4vXridij5hbUpqKIwV8P2ol8b5VQPH2BtIW3hfvxBXORfP/su5XFx6W8Y5BF0siAUhd5EO5uXfE5UGAUf1aNYecl3KRuS5cegEhyqkMpFRVx/fv/tBSMW3y/WzYWifAdxBGJ/2asouOWHCH4xSmkhIDopU2/84m1V9UGX4/eGJebeU+551v8tdpKRIFtGEHjJfANXqczw7LLNkWk/ueYtgmcI45NvhnLfji+VzINLhMo2d9vTy/Gff3/VdzwvqqepBb9onJI1S1E+XvUBr0ZhGK4A22O4l+cOQqfEvyfV+D0DLkDwh2nzw7vscMHSKY999UQ8eOnxOHDPYYqrJI2fpIkgJLxCURKcHL4wu9I9y1SOevetpNFLk6jv95i7rMW2+qieNiOW8CAiHGQ/y0WrtuEPTy33af5xwoGUAvz4wxQN8be2gqEMWdFfVgdPczl+f7kuxy+t+KTonHyC4EHGqtX419uuLnEMp786z+sMSLBsQa5nV5Yaf3UpMVWKyVNvbcLjb/iTQ2mqJwWIVA/v3GfZybJF7xefz7PhdvjutsrMIEqqKKRvih2XC0fe2bgWEKZNjxyk3sW554hu7BOycUUW9GEcv7g05dfJ50RlDZKFkooa8u32jRCkccNriPOH7OUSV+MH4ERP/cLtC/D1P7/key+cBgtD0M7dcKrHED6rNf7+klrw83pUz9L5TfH+xRrk2qK4eRkOxy+980sDNhyK8PVh8q5esqV60uf4gyCng8wKzS34DTfbk8kYhnYWcaZtKBPHjEwlFMgN4CWGQgiDqPUVA3aFxhUsvBMv32SlceMGx2njggV4FE8aBLFJBnmFo3wP4oDl40ymDuRVify7/AyShl0A/GGUq9H4+bHu9kJsrVG+hw2Sk/bUMYOw8DvvCS2D76WIE5ZYbjNge/WYTBH6OUjwB7eFT9bFgkz1kWcilyf1pFo2SQoNR5xxIa+oOcfvlpGoKYlQNChWXuwghHnjydBePSlAdEdjzIqTwjUasROrtrc7Rr+YQkUcE0Ghb+MKfn4en0zOP7oHw7ra8NGjpoRed+y00Thq71Gx6uDwefUoOH5r5eTV+Pkglm8pSuOXzx+oQJOS+VbVpMcQHpiPf+bPuqu9mHiDHceabV6OumgYnnAGd33mGJz1i8c956zaYl3ja2NIdxMVFG7vKZnezXSlsjpqJvfrV/XBIFdPkjR+/yQV3NYgiJvtXH4+uiBVSHGv0pKd5DcMUkbnjIskAR/lCS4rNLXg93D8zCvYRA1dfjFiJ4qrSYsDWGXYBeKH9Zc1tuFdbYHxd0SI28zjQh683qW+bfgsGugdMD2atkP1SAVEeRX5Nf5o464M2SAalFNVbotH47ev4QKxq60Qf2KWXu/67V6NXxa88mCeOnoQ3rZXcyYDjugZiaFdRTz4yrrQjUiecApCPxb9CvrKpsftkyOM4xe9ekQQrPFz70urccDEYT6qpxJe3SBy7EB8DMahaeSQ4gzh9qg0UTQoMM1lrOsTCH7Vu8sCzU31eDh+a5OHo00L0kMWXgVyqZq4NIKH6qla45e+Z7iOJWnwiN/5J+6V4OX4vedw+HYOSyfIjyDJxhgOmRcPekd+o6v7ebCtQfJ76mqPZ9wFoukqede3rK1OHNHlCTfQ0WY4HjJh71qVdF5+FgNlf8hswF2Jqbqg68cv03KWQvOpW5/DaT951Lc6qUjjVxyLMy58WjOT+27ytsRFwaDIGFRhSNK2KqLBJ0KTC37yGHcpQOP3XWe4LyuuP7+X6gnQ+GM+bV+Ygwx7tcyTqoJ0ceNUn4fq8Z7DIctxueXyd5XRLEqTlF9d0FLaJ/gl11XAvaeudnWSGxWiVi3yik8Op100yBOPnwROJUzjF9+VQ1lKz4IxdX9x/fhV/L9f8x49uN2mSq3v2/tKvpVWJYnRVfXH6d/yu2FgntqzVI6q9eoR7/mAiUNDztQafyogco27zNb4uYwITZsmcPxx90OJ5QVNFpV2zazikACS1mR4vTrEzU2AmuOXb5Vr/N896wAAfm1cHsCVGHfldxdEx/l2BSveiyP42wqhORpERGr8Uj1ikvsLju7BQXsOd2La837pCOYQAUaKd6NSYMK8etQ7d73X3f3ZY3DvfxwHOR6/L2lOJdJDcXuVaLmM5Uf1qJ5nkBedCmLTxLhPKiTdOFopmlrw82fIGHMi+PEOEmaEbC8YjjYTN166R/BXSfX4rsvwLXn9+MkXpAtwBWufYFR17kW6Jc6r81WCjzeWzudCU8yOFQU/x6/itJnCC8VfFhecnW1G7JjokRy/9P7FFckVZ+zveHkMlE1rJQpxE1W8PuJQPSbzvBdALTz4vSlL5/y/fd1Bew63gg2SV/HxcfyxWuqF6vYqHRd5GXfl5/nV2ftiwrDo/T2uh457fVQIalWQwizQ5ILfXQ5z4+5oexfgoZNHeM4Vc3B2thU8IWjjQNS8Ao27Cd7nby9wA6BlqfGLA4bk7/ZH3ln7FBx/0AYu3mZ50Mj0AF9C/+Wzx+C178122hEGWcuNzfET4b/OOQTXfeRg37lFw/Cdv/h771WWK9/zI4u9OaH9k531nQe94xPBQNm0Uxj6w3VEQeT4d0rZodQbuLgHjb8sJx6/9KMhu3P6OP7k/VJFD8UVdK99bzaOm26lYbU0frEtiZsSG/J9miw4+9i/vnOy83m4bbcRL49KXlMwyBdgLws0uVeP9d+0NX4iYNLIbtz/xeNCNcyOouEM1rhBz8QxkVTjV8XnEDtWfhy/2p2zQ0H1uBu4JMEvbUyS2y7fCp9M2guGM8FEyRM/1aO+QBUAjgc8k1EwyOcFFEQhRQk81YadR79yomPA5QK2VLZWJUWDYlE9Ipz+yRj6+qMF/1F7j8bvnliGgxThHIKMuwSvZ1SS8BJBUN1e3Mmuo1hw3FgZ/DRlVvCnGQ2O/z97//H4w1PLAVghLVZt7UWv/X6O2GukE3wvCAUidLUXsL0KL6I4aGrBzzsGj+DHX9b0cf6HL77IYsFw9JK4VI93A1f8hdSI7jY88bWTfcfDgqWlCa8fv/c5cAcdh+Mv+427csu4oAgKVufz6rEFv1fbDL/fOMZdJrQ/qG4RBUOd0UuFKBnDJ7B5Xz7RCUswaaSb3IMb/wdMEyXT2nDFn1dUGggi4NwjJgv7Ufx9VDXxzD5gPF749qnKMAv8ecrCUxZusldPJd1SubExgdB2V+IsN6pHNrgGGdDldhw3fQxeXbPdGT8HSYHz1HVRbE/CatASVA9jrjtn8Lnq43GNOOLgC/Ir72wr4Ltn7u87poq6mQfPB/h5Um/YYS9fL457CtL4TVnjj2fcTXK/sd05fYIquA6DAoKeqc6NaCt/XpNHdeOwKSN8v/P+MVBmFgUpaPxRz+GtH5yO73/gQMcgWmbMNxEGRXGNiq3jo+Wkpsj1VCb4/ceSCW1RUfEqLVlBHs5hiV/E7v7V2fvib597F6bYITzi9HH5nEoztEWhyQW/9d+0B0dYB+OD2dFk7f9nHrIH/uucQyLr8hp3gx/rR4XsV0CwDSE3677E6YvVlh1DrV+QOH780q1yjZ8LXT/H78VA2QRRslWNLPiDnnfULmIRBYNCczSIiKR6InZf8omqVLY0/qJBLgcf872LTgr+HK+VDWu5bvmdvLhiq/f3Csy7qisq8uqRyso6LLMIk7FAhws5LMgBE4fhuOmjAQCn7j8usi4rQq5YV/L2xkFmgp+IbiSidUS0UDh2OxEtsP+WEtGCrOoHJOOuGZ6QWd6wJXLYQbywCI8ffwqdsFYavzj4uSBUCTL+fORWcndO2UXQrc+v8fu4ZeGrimeXBXq7aoXFkiWlKRDFpvXiUj1BcKieMoNpSsIi4V4Ci8aUBH+FxkEVxy9CjldT0QYuFdWTYNIXnS68SkuWgt/7fdTg9sDxqTq+/x7DsPTq03HYlJGKK7xoL5DnvpImVoqLLDX+mwDMFg8wxs5hjB3CGDsEwJ8A3Jlh/YIvvuvOGXiu/Z9rS/x7mIeECC/VE/+xyrlROZKmfqwUssYvDn4uYDtU2cTIfz0gJBix/0fF0u8vs0At94dnH4wF3zrFd1x+/KrJYf2OvtgaPGDTLXHdOSsw7opw4+yYKFdo3BU3IsaleuKWySHfpyrpfVIojbtJOH7nk8zxJ25KbIj3ee2HD8K/vXNK4L0nacehk4fj3ft5VwEdxUJjC37G2DwAm1S/kTU9fwTAbVnVDwgcv4lIwS8m5LDaaB9XbobxXx8nZEMS5KXxh3v12M9EIciCOH458U2UH39/qRxIBw3uKHry3Tp1xKB6vvLHFxNTPXkJfkfjLzGUTHvic4y7MTV+x53T/zw6K6R65Hcl92P/ZrzkdQRp/KMVyVbU11v/nR3PNvJyef7gO/YM9bVPMhmee8Rk/Os7J3mOyZngVDkX0kCtvHqOBbCWMfZ60AlEdDGAiwFg8uTJQaeFwsfxhwhT/hPv7Jy/VHUoK/StOpk1kI62nsbkEQfi7Vlcu/udCzCVIHOoHqmZbkpB67v8LHxhnMss2FAW8AgswVl26g+i1hJp/ESBqy/fuRGvN4p24O92wDRhMq7xJ9vAJfZtWStMS+OXv/t27qao8T/21RNjpQ0V+49YVKaeb+IYsf8H99n47SibzNduOS/Eik27MXOPypLah6FWxt1zEaHtM8auZ4zNYozNGjNmTEWVuFqRuzU+8FzyCnr+7MO2+YvwbOBKQWhn6Z4WVI+ciMMR/ApB4hh3pWby53DAHlZMkiOnenlN+fwBM5jqCRKC4kQkpsmUkYjjT6DxV6tdOvmRywylstedMzbVQy7VI7e7YuOudF/yhBrXBhIO//0VDEJnWyFyc5MIhtps4ApjAoBkK/WyyXxPo73oDRa4WJE7Og3kLviJqAjggwBuz6EuAN6du8Hneq9xvivO/cXcN3zH4nr1+K9TH6+FV49M9fAE06MULq3OAAjg+I/YaySe++YpmH3ABOk67/ll0584JKhsDtHYbIQsu7My7larXbobuKyQDZ7NegmpHovjT8e4q9q5KyINvln1qpIoOXy1ZW3IFJ5bTpsceZ1B7ylJ15DvAbA3jwpSRw7HkRZqofG/G8CrjLEVWVfEX5gbqyf4XP4CZKpH1dWvn7fEd8xj3E3QCYNkTV4cv7xTV+yIu+1QtOMVcUmcCVI6zr2niEi5B0K+rVLZb3vhzz5oEIleM2IIbRlJBJVhqN+18tyQV/O3z6mT2ovgikF/2b+BK67g4IKH71HxlF9h34ni+KsIUOlAdX/JjLvufcv2qaygjCiqWNXvM3ZwrHs5306oVDb9Mknm+PvTeOgKZOnOeRuAJwDMIKIVRHSR/dO/IGOjLoccqyd8A4/1X6Z6+JjiMUKCECcDl/q6AK+enDh+cckqd8IhnRa3OGaI3/DmUGMGYZCQLq5kRnlPeX+z7CXSOVEav8+7RF1XEmoiEdUTMrj3HhOcHpODU4El252zIHD8cd8613zLzK/xVx4M0HudfJ++XAuV1KESoknaq9C+rc/VtCqiSoU9S27zy1e+B3M+/y6f/FBBXK3J4+GgPYd7nlHc3eRJkZlxlzF2bsDxC7KqU4ZoAIvL8fOX4ngE2QPy5o8fgQdfXot/v3m+8nqvV08SqkctbXLT+EN8oX/10cPw0CtrMWFYl+86l+MnTBrZjVfXWFykircUoTIGBxnD43D8DMETjcoWE4Qkwid8I2D09fx+SzxkAyXX+J2EQgp3zkp9C+SVgvw9DapHdXuVtJdBEsQ5UD1iDXJ93PuMjyFV/C2OC47uwYOvrMX7D94Db6zb4Rz/5PFTUZA2cMXdTZ4UTb1zV4zVE+nHH6Dxi309zOuAVUj1BLkc5ubHrwjDzDFxeBc+dlRPJC+75wg3Dk05QuNXUj2yxs//BxTzyeP3dj4zFqwl7+iNH+iqkngxKsR5bzyoXL8dsqEg+PHH1fm54FGFn67U+Cy/N9+O1RSUz6o3cNn/5UBpeVA9cerj7yVM8E8ZNQiPfuUkjBva6Z1MHPrUPZqVO2dTC35PrB4zQlOTNH4OUaCHaTzib0my6NSa448T70T13MRDIhVUjtghLQs21c7dsHoB4D37j8dXZ+8LwL+DU0RvRhp/2LuJ89r45NBn74RVRUSNQpjGX6nx2e/O6f09iXtsEKrl+E/dfzwAYOaEoZI7Z5UNCwEfzt4Vhvv5dx8/wm2H/T+uS62c+tT67/4+UMpG42/q6JxeP/6okA3Wf7685S9EfOyzekYAAIZ2qjYVuZ+TxB4JonoqdclLClVydd85ioEpdtgxg10jbsk0Yz1njnIF7pxWW4PL5JBDDISBZ12LI9uCntOX3zMjltDl9hs+MSWxL8htKDO/O2elOoNf8Hv7YDpePdVp/GccvAdOnTkOnW0FPL98i3M8jyx1oibOn1V70cDxgv2PBx3sao8r+N3PhiR7AGs8ZYEmF/yc6gkPpSqe63L89g9CXx83tBP77zHUSaghQhTgUYP/fy8+Emu39eI//ndBoDtnXoLfI3QDmq16buKhUcKuy3KE26z8mzpWj1/zCSsn6HknEfw87WQphgQOur3PnLhPrLr4Dlivxp/MuCuGbFiyfqfyt6TwefVk4MdfrcYPCNq0QmhmAadosb4ArzYeunxkd7yovuL1qr0x1eT6DUNTC36Xp7c0/jDunf8kG3Lkzl4w1P7eXsEf3q4jp47Cso3WYA1aPme5E1GEKrm6jCgtrVPwqy+bZoRXjxdWBirv0RGD2rByy25f4nZPOfYllnFXfc7u/mjBz7X8AtkB6mJotdVql1zwb7dtEEWPO2e8svmq8vp5S/Do6xs8v1XKd8v35ffqYRje3YYtuwYqKj+obZU+T5XQzAIqIV9wFERvxTMnDMXnT9oH//rOKfHKVoy/PLx6mprjd+iaWMZd6zfeCbkro+yhQ0RKf2ZRXsQZeLzcrOJtx4WX6gk4J0LjFymBUjmhV0/ZL/j3nzAMALB5V39gOXEMbb0D0YOGX2kY7j2dMnMcbrxgVqy6KwGnen7y0OtOebwXxC2Z99cFb29R/FZZu2TTlMqrp9pJT3V1pX4M4sjJw7jroWUCVqVEhEtPnaHc+6ICKT6LZd79wiqs296bsMXRaGqN393AFe3HP8h2x+q1d8p998wDMGP8EBy7z2jPeQVSC2uR/4xn4HNpqFpC1ZllqAa7+CxFARFl3PVRPYqdu998/0xMGN6Jk/YdG1KO9d8K1qU+Z1d/tFcP2Sp/gdxwFV+dPQP7jA1OkVetkJFzMleyZ4O3VRUJtlKqR/ZIkumTaMN9NNKgejhMz5jLTvDzolUcf7X1RnH867b34ZXV2zF2SLyJJC6aXPC7wjXKj3/EIEvD58vvYd1tSs7WIFIaucTJIJbG7wj+Gmv8Co+SP33qaIwb6vL2crIVwHuPBUnwh/Kt0k8qr5zBHUV84d3TQ9vt3byjrm/r7mhKgl9p+U/bq74IFVT1cxLhJQt6g9xELHHlCK9PFReq4g1c0mU+jV8RYiApqnXnFFHKSfCrNP6C4T9WGRRKlfQ9i/AtTS74rf9xMnDx8ALbI3y/jQCOX6TiYnl2GP50hrWAZwOX3eXkdIFKjV/4LHbMqJ27So63go7t3a6vPieMKvKVZ7gJMKLojGrvQRUTx6F6YhbDz1OHzI7dFOk674W+6JwRm/Ni1aE4VrHGn8CuVg1I+g8Eu38nhco7zb+fIv2bawmO/wf3voo31u0I1/htK/xYRXgCEQapN7KYLCHVk1NIhiiEhWzgUHL84sYvmeoJqU858CsYtaK7bVAKwDhGSF61GOUzinNWCf4km/aIyKOpFwxXAYibztDV+BVUT0pSUKZ+yhF2sjhI07ib1a5WGSoKhk/e1VM9fsUrytaSBppc47ce2LzF6wGEa+KdbQX8+qOH4ZBJw0PLLBiEUtnEVXNeRl/JxJVnHgBAFvzRLyrOLP7iFadGnpMmgrQX9QYu/yAAgJVbdocm1UiL442z8Swe1UMALAOzGH8otG7FxPD7f39nZF0iioaBgTLPKSCqffGu521V50NOR1D4Nf7qvWdUTau0ueKYixPLv1K4HL+L7g7ruSfZHa4sW/jsehZqjb8qyM8r6vm9Z//xGKfw0feWYVE9v3n0Ldz8xDLnuGfZGaNtcdIzDu1sw9DO9JMwBCHo+ah4ZNGm4U/ZF1ZHulQPC+Gd41A9suYdr25/fYdOHqE4Mxjiik+keuKC378ySU5KgkLlzpkFx19pmaKwTyOAXBAMheQ/aOJwAK7ffqXwzPkBjyGL8C2xNH4i+pbqOGPsynSbky7kAZqGJqRy5zzsuw+gXwgPEGfgZel3XCmCBqDquLixxJdlK+TeVD9VIqjiDJituwcwpLMYarf546eOxj0vrUZH0fAkNwlDGv1InPgJwGjbxtSdcKu/qq1p9S2VcbeYgTtnpRDvPUvaR6WJHzxpWEplK6ge6RlnQQvHpXrErYGdAN4H4JXUW5My5D6axoCV3TkZY9i406tZxqmGD9yPHRVvo0ceiPN82guGFUe+HKbxJ5P8lfRrVYwTGb0DJkYN6ggV/PtNGIr9JljZwg6dPAKrXlodGWclDcHq2ThnAN85c38c1jMCR+w1MuQqsQ3W9QMKjTMrqicNd840lVfTo/FnKfg5x+8eG9LZho8fsxfeMWV4avXw8j9w6EQ8YtPTQA05fsbYj8TvRPRDAPel3pqUIWuqaYwH2Z1TxS3GHXhLrz69+galiDit7movoH+36RE4KvfEIKRH9VjXMERQSwkEzQ/PPhifOG5qZOLvNHZVi4PZIMKQzjb8W8zdntY11n9V/0v6PC977764d+Ga0DYC0ZFX4yCu8ToOxF3vE0f4Q4enhaCkQ996/8wUyvbXc9ahE3HWoRPRc9kcANlw/JUad7sB7JlmQ7KA/LjS0IQsd073e5ZL7bwR5/l0tRWwdfeAh9tMlkGpsnr91whlJrQpBKGrvRBp3E8L3v0TlU98Ko0/aXGXHL83LhFCXXNk4c6Z5tjgGv/5R03BlFGD0itYQh7hIIBgxauWHP9LcHdIFwCMAVDX/D6gonqqL9Ny50xH4683hDW7aBBKJnOiDno0fpnqCemnKj6/Eg5TDLkdnlmtPt+FV+NPfj2/LRW3nRnVk4I7Z5oO93zsqTLEpQlxdZk24tiqVGkeq0Vcjf99wucSgLWMser8mHJAFsZdOUhbWTHw8gqwljbCnk9bwUDJLDv8d6Ucf1oav3hJnAQ79QaPxl+BHh2m8aflx58Jx5/i++BUT5L8F5VADA+SNsR3H6zx147jX5Z6zTlAflxpCGTLq0fU+FXGtaqrqQnCxg/vfGOHdOCV1d4do74YLwkFcSUcJsVYIke1pZYQn1kl/YXfl2rFmdYty+/VTCFkQ5px87nSlST/RSUQgz2mX7b7uZK8FJUiy2TrNxLROiJaKB3/HBG9SkSLiOiarOq3KvN+TcUbg7xJM9Qcf30KmyiEaZ6cjvn8ydNw+Wn74ezDXBOP3DHD7l4lOCoRBt6QDWFUD3DxcVNx2Xv3TVxHllAZ9ZKA3/+AIstYWitOlcZf7RiShVs1TT1+hpUA5Z17jaqmSZHIkurx2KoCzmm0nbs3Afg5gJv5ASI6EcCZAA5mjPURUXD4xRQgC7JUjLsUvWOwQeV+6KDmy+nu9gI+cdxUz29yx8zDjz/Ozl1+3tdP2y9x+XmiMo7fpnoy3LjkT8RSvVdOmhr/sdPG4I2r3usLnZ42nMeQicdoNMmfxf1l9sQYY/MAbJIOfwrA1YyxPvucdVnVDyiMuyncrezOOfc1/y00Kscf1m6+w1W1izcRx6/4rRKNhgK/8HqC66sHxEmAEwbHnTPLjUuK91Lt40yyOoyDrIU+kKNxN+CcLDT+vEM2TAdwLBE9RUSPENHhQScS0cVENJ+I5q9fvz7otFBkwfEbhpfqufzPC/3n1KesiUS4xk/2OQrBLU0G4e6VimNVcvzKNjntTVx0LqgkwboImeMX876mBZXAqZrjT7LZr07Am5gFx+9NIao+p6E4/gAUAYwEcCSALwO4gwJ6EmPsesbYLMbYrDFjKuvUctFpuXPmsaW/Fojy6gHUiWOSefXkw/GnlSgjCv9x8jS894Dxia+Lk0Es7vWjBrXjdx8/InEZUYjKvJZGmVkGV0sLmWr8inpkZJFIPu/onCsA3MmsqfNpIjIBjAZQmUofAX+QtuofYFDO3bB6GwVhz0dM7i1DjhAZphWm5dUTpSlZHilm5u/ii6eEJ4wJQrUafx6JxlUafxZhmesdmbpzxqB6sni/eWv8dwE4EQCIaDqAdgAbwi6oBv4NXNU/QKJowV+vvHIUwpp94TE9AIDxiuilcoTIsH6qqqMijVfMBxAymdTruyhUrfGry0oTqgm5eo6/uutrgawmVkDy45eq+cSxe2VWb2YaPxHdBuAEAKOJaAWAbwO4EcCNtotnP4DzWabZxtPnEwtEkXlyG1GrAcIH9b+9c0pgLBlZ8Id79ahomVjNCywnzGBcr6sv78RV3YonCw4YUD/XtDn+RoCb9CdbP355bFx++kxcfnr18YBUyEzwM8bODfjpvKzqlOHX+KsvMx7HX309tUClE5bflhJcjjpfbXLJH7VEzovjrxRpGXflsrIGAbjxglnY0Veu6Pp6fR9hyI3qyfHRNHUGLvk5prFkIyJPrB71OVVXUxOkNSjDSklL448yjqaVGi8rxPHmCINnx2eOt2gQcNK+4yq+nk9Se47oworNu9NqVqbI1p0zfOWaFRqQcYuPLMIyd7QZ6IvIulPrBOqVIg8BojTuVkl1KL16CpzjT1x0Lqjej99//Yju7LO1VTuR8nedhftpVshyA1ecnbtZoLU0/hSkQFdbwZNtS4Usk0Jkihx6Xlp+/KqwzDyCKAC02fRRvWr8aRp3+eUPfemEWOkmq0G1j5O/60bi+jPl+EOMu1miqQW/Pzpn9WV2t0enxovy+qlXpCYkQ8tRaOcVcR3+6gqC4OfHMg7cWDG8G9CSX28oKIKRg9ox0k7hmBWqpSNECm7u/zuhIZSkLOWxl7LTVE8qyOI5dsXIidoAfVmJXDh+FdVTRTx+8XPBIHzupH3wp08d7RyrV41fRLUcf553WG1dosa/1+hB2Gfs4OoblTGy5N7FkvPsqk0t+GVEUPOx0F6MfmSNoMWoUM2K6NJTpit9/P11pKPxq4yjBYPwpVNn4LApI+o+Vo+IStpIRMI9ptygEKTF8TcU1ZNl2TXqn00t+OVnmsaWgd6B6NmjUameajrh50+eho/aiePD/fj9qGznrvjZ+iLuNOXcaSPIl0qFaS1WNdVv4GqclRgHpwuzd+fUVE8qkF0H09DEd/RFJx6LcvesV1Qda93uuGHFqAZ8ZRm4/By5yje+EQRMpc+9FpNaWiEbGmkHb5oJ4v1lu8jVLTe/qvKH3EfTkMf7jh8SeU6GkXIzRbUaR5zLRw/xGx8ry8Dl+eYrhxxtOHHRuaPajXN5aopphWzIKsxEFsiyqd5k61rjTwV+wV+9RD55v3GR8bFbVeOPc3l3exETh3fhg4dOdI5Vk2zd+myXo0hnWK8cfxrN4veY5+RW7fN06KlGmJFzgN65mwFkTSot7n3KqG68uX5n4O/lBuX4q13GxzWoPn7ZSTBNhjufXwnA9blPAq8fOxcm/rY0s3xxqLVcjbvplNNYGn+WVI+o8eeHphb88oNMS/DLSahlNKpXT7X9m3fiOMWIdVWr8fPn7dX4szUi3nTh4WivMVFNzv8cqZ6UymkkjT/TptbIuNvcgl96jmm4cwLRnTbTgKMZIi2NP9657smVpM8T6+ITuofjt/9nJfhPmFFduug0/Ldro/GnU1kjGN05spxYVTuw80BTc/yyfpKWQI7SANKaYPJGWv0uaQduqyjnrnsNzztbVBh361W+pNETa7FXoeqq6vR9hCHLx+sJ0pZdNT40teDPwrirKlfG0K7GXEhVr/FzqidZOZVo/CLbxqmeRnXnrBR85ZnnHVbt+WW3tpH2uuTE9GiqJy3IjzE1qifgBZ124Hgcs89onDNrUjoV5YyqA3BVeH21HD+/fsyQDt/v9Uolp9GsRjTuttnvqtRAPs9ukLYsyhY+Z1B+EJpa8MsCOi2qJ2hmbi8YgVmqGgHVa3OVoVqvnn3HD8H3zjoApx84wdeWptb4OdWTQ11E1s7VavluboAvmY3Dh+blx59nQMGmFvw+427GHH8lmaSaCc7EkZTjr1LjJyKcd+QU5e/N7MfvblLL/h7bDAP9ZbNq4dRWtNra30CGsLx6kN7AlRLkB5mWl2XQ62mkbehZoEK5XxHH3xUVHtsxfCYuOndUOuCNHO/RSV5fpXDiq7tGpHqyKVv8klk1PmQmqojoRiJaZydW58euIKKVRLTA/jstq/qt+rzf0zIoBWlYzUwrxEHFVE8FGn9UeOxa7GrNG25spOxvkntMVdvF+bseaCCN3825m/5k5Q3ZkB+y1FFvAjBbcfzHjLFD7L97Mqzfh7RCKbS6gA9EQmMjF95RG+KU10Zo/G50zvp/V5VmdjIqXWJVAJ4zodrnyVd3Aw2l8WdYtvC5KRKxMMbmAdiUVflxUCt3zlYFOf/jPaBBHZaJqRKNP2rXLJ9L6pXjTwN5hqVIW+MvNZDGn2l0To+tKrNqfKgFK/1ZInrRpoJGZFmRPOizdudsINdkDz59wt6plJO04w7uKNjXJe/xUdc0Ujz+yjn+/KietOLotzkaf+MIftdelP5z9lL8TaDxB+CXAPYGcAiA1QB+FHQiEV1MRPOJaP769esrqkwe9Knt3G0yI+5XZu+LpVefXnU5Sf3Kuca/u79cdd0y6n0DlzjIJ47oqqiMPI27nI6rtqq9Rg8CABwwcViVJeUH3oey4PhrFZ0zVxHGGFvLGCszxkwAvwFwRMi51zPGZjHGZo0ZM6ai+uQZNK3OVq/CpNZI+lR+fM4heO8B47HvhOgcB4nbUucbuDh+du6hGNbVVtG1eWbgcrx6qqzr0Mkj8MAXj8PHj9krjWblgiyfbq2onlz9+IloAmNstf31AwAWhp1ffX3u5xsvmIXjp1cXWCsKlRrpmgVJO+70cUPwy/MOq7i+Gy+YhTGD1Xl+Ha+eOpf81Qx2ylXjT4fjB4Bp49Kf6LNEXgI5T6onM8FPRLcBOAHAaCJaAeDbAE4gokNg7X5eCuCTWdUPeGfqmROGpZbgWWv8ajhhmXN6PCftOy6kLRbqNe6765BTefvyMFzf94XjsHjtdvz0odcB1P8KKgvkJZCbQuNnjJ2rOHxDVvUpkRF/FtT5G8lelQlSEGZpwc3tWvu2qMDp4mr6ZR5ZxmaMH4IZ44fgF3PfsOusz+eZJRw//ozraRY//pojq+w2QZ1/90B0IvZmhuPOWQeywTHu1qngTwN5BqLjgfDq4d3mjpzuOc++2tyC36Pxp/dQg4ralYF3SiOhvnzmbY2/rtrkIs1YPXncIY9DVV/vOB/kRvXkUouFphb83kBe6ZW7z1i1cWpXX4sL/lo3QECjaPzVeAjmmVDeMe5mXlP9ITfjbrO6c+YNCvhcLb506nRccHSP7/jO/tameupxf0Mza/xGrhp/fq6j9QbXjz/rmjTVkwqyonraCgaOmz7ad3z2/uNTq6MRUQ9GXQ7m5OGtcUMyRC00/jpfQGWCZtT4mzsef0bGXcA/2BZ+5z3ojogY2eygHAVRFLh2VvdUTxW+InnmFU5rA1cjgt9x1l0pz9VUUwt+Udqn/VDl0gZ3NPejTIJ6EA08IF+9Uj1pIM8MXGlu4Go05KXQaONuSsgyyUErcp1RyFMDjQLXo+vVjz8N5Buygcfqad7nGYS8vKe0cTcleOR+yg+1HoRbvaGeHglPvdDME3SeydZbmuPn/zO+92aOzpkrssxu08wCpVLkmBckEq5xtx5a40cagzzPWD2FFt7A5Wr8GVM9WuNPB+KDzIrjP3TycLxypSrRWOuBD4x6ELaNYtytBrVIvdiKCk9uGr8W/OnA49WTOtVjFVg0KDrxd4uAP+O6EPxoDONuVRu4nCxj6bQlDC3t1ZPTyqopUi/WAzx+/ClrRS3Y/yPBPWkqyaGbNkw7YF7d+vGnuYErz527Ldjv81pZ5akw1euwSB2pa/zO/xYcCQEoleuHV+cafytQE/ns3LVERR282ppBa/wNgjzSmrV68hURJZNr/LWXDtyrpx4moaxQC6+eVlR08nJayLOrNrXg93r1tF6HzRtlm1/hIXxripYQ/Px/Hn78rezOmY9hW1M9KSFLP34NPwYcqqf23YrbG5qZ6skzSFvRDQyUQ231Bac7a6qnMeBJZFzDdrQKyja/0lYHGn+j7NythiikvDgIaI0/D+hELClBfIxZzaaaQnIxYOeerAdhW+8afxqtypPq4ZNMvT7PLEE5PWfN8aeEPIy7Gi7KdWTcZQ3C8bMqHPnzpHryDAhXb8hrA1eee04yE/xEdCMRrSOihYrfvkREjIj8Qe3TbYPys0Y2KLP64fjrPR5/Gv2xFhu4WtGHLa8gbc1C9dwEwBfLgIgmATgVwPIM684crTgAosD9+OtC47f/1ys1UY2mz5FXDBmxLr6qayXkFZa5KYy7jLF5ADYpfvoxgK9Ay86mg+PHXwfGXXcSqlOVPwU4YZlzuEVOQ6QxYTUaSPqfFZqC6lGBiM4EsJIx9kKMcy8movlENH/9+vU5tE6jWpRs4249aPw8//HgzvpMkJMK1eMUkf3z5nWVW1Hw5xQag3KUxrlVRUTdAL4O4FtxzmeMXc8Ym8UYmzVmzJhsG6eRCt41zTLZHLV3pqabWNjZZwn+IXUq+NNAnjt3Of9sz+0thby2MOSp8ec5KvYGsBeAF+yZc08AzxHREYyxNTm2QyMjHL33aLxx1XtRrAOL6vbe5hf8eeY/4MZdsxU1/rz8+JtR8DPGXgIwln8noqUAZjHGNuTVhkxQe1ajrlAPQh8A+kqWajqko63GLVEjHT/+/HzrC9q4m32y9WageojoNgBPAJhBRCuI6KKs6qopWm8cNAQmDu8CAHS21cdElAXyjKLgUj2t2+EzD8vcDBo/Y+zciN97sqpbQ+OPnzoKr6/d0dT7N7ggyjNWT0tSPTlNsE1J9Who5IkJw7owYVhXrZuRKdwNXDl49diCv9TSGn+2aJYNXBoaGhmC8vTqsetoRT9+fsvNtHrUgr9aNE9f0KgBqsq563j1ZN8Ji5rjb6p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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "turbulenceData[\"y = 0mm\"].plot(ylabel=\"u\")" ] }, { "cell_type": "markdown", "id": "restricted-preservation", "metadata": {}, "source": [ "And also we can get the main features" ] }, { "cell_type": "code", "execution_count": 11, "id": "dynamic-internship", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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y = -40mmy = -35mmy = -30mmy = -25mmy = -20mmy = -15mmy = -10mmy = -5mmy = 0mmy = 5mmy = 10mmy = 15mmy = 20mmy = 25mmy = 30mmy = 35mmy = 40mm
count1000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.000000
mean21.10436721.04447320.75732020.31643520.24730820.27057319.73393719.49343117.79897517.05982019.13861419.37730719.33013519.22875219.02617519.12156518.570242
std0.1872260.2285230.7620610.7765830.5367620.2624420.2511070.4915381.1245470.9889070.3057860.3547260.4620510.4781660.6947880.6624010.860208
min20.46890720.20728718.63479818.86666219.12360319.70476019.16860818.29722612.82460513.76581617.23492717.76428617.24515517.26565716.37357716.51118416.101291
25%20.98939020.98939020.32284519.75101219.79736520.06585319.56659619.07589517.32729416.49146518.97798119.21371019.10957218.98916218.67876018.72281517.983749
50%21.09984121.11216820.73369520.22501820.27239320.21909419.70476019.53217718.07167417.17357919.16860819.44070819.33825619.25890919.04505719.25890918.689782
75%21.17382621.18615521.06297720.62498820.67625220.49284619.91368319.93702218.56903117.77479119.31556019.60103619.65860619.52073919.47780719.60103619.227838
max21.64780221.44703823.72765823.15710521.77420920.84289520.36148720.66114019.84381719.72787420.07762020.23094320.72157420.44499520.83075220.33769120.492846
\n", "
" ], "text/plain": [ " y = -40mm y = -35mm y = -30mm y = -25mm y = -20mm \\\n", "count 1000.000000 1000.000000 1000.000000 1000.000000 1000.000000 \n", "mean 21.104367 21.044473 20.757320 20.316435 20.247308 \n", "std 0.187226 0.228523 0.762061 0.776583 0.536762 \n", "min 20.468907 20.207287 18.634798 18.866662 19.123603 \n", "25% 20.989390 20.989390 20.322845 19.751012 19.797365 \n", "50% 21.099841 21.112168 20.733695 20.225018 20.272393 \n", "75% 21.173826 21.186155 21.062977 20.624988 20.676252 \n", "max 21.647802 21.447038 23.727658 23.157105 21.774209 \n", "\n", " y = -15mm y = -10mm y = -5mm y = 0mm y = 5mm \\\n", "count 1000.000000 1000.000000 1000.000000 1000.000000 1000.000000 \n", "mean 20.270573 19.733937 19.493431 17.798975 17.059820 \n", "std 0.262442 0.251107 0.491538 1.124547 0.988907 \n", "min 19.704760 19.168608 18.297226 12.824605 13.765816 \n", "25% 20.065853 19.566596 19.075895 17.327294 16.491465 \n", "50% 20.219094 19.704760 19.532177 18.071674 17.173579 \n", "75% 20.492846 19.913683 19.937022 18.569031 17.774791 \n", "max 20.842895 20.361487 20.661140 19.843817 19.727874 \n", "\n", " y = 10mm y = 15mm y = 20mm y = 25mm y = 30mm \\\n", "count 1000.000000 1000.000000 1000.000000 1000.000000 1000.000000 \n", "mean 19.138614 19.377307 19.330135 19.228752 19.026175 \n", "std 0.305786 0.354726 0.462051 0.478166 0.694788 \n", "min 17.234927 17.764286 17.245155 17.265657 16.373577 \n", "25% 18.977981 19.213710 19.109572 18.989162 18.678760 \n", "50% 19.168608 19.440708 19.338256 19.258909 19.045057 \n", "75% 19.315560 19.601036 19.658606 19.520739 19.477807 \n", "max 20.077620 20.230943 20.721574 20.444995 20.830752 \n", "\n", " y = 35mm y = 40mm \n", "count 1000.000000 1000.000000 \n", "mean 19.121565 18.570242 \n", "std 0.662401 0.860208 \n", "min 16.511184 16.101291 \n", "25% 18.722815 17.983749 \n", "50% 19.258909 18.689782 \n", "75% 19.601036 19.227838 \n", "max 20.337691 20.492846 " ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "statData = turbulenceData.describe()\n", "statData" ] }, { "cell_type": "code", "execution_count": 12, "id": "certified-return", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "statData.loc[\"mean\"].plot(title=\"Mean velocities\")" ] }, { "cell_type": "markdown", "id": "cb0a01af-7b65-4d0d-8191-9c51c0cb824f", "metadata": {}, "source": [ "## 2. Computation of turbulence intensities\n", "\n", "Remember the definition of turbulence intensity: \n", "\n", "$$ I = \\frac{\\sqrt{\\overline{u'^2}}}{\\bar{u}} \\tag{1} $$\n", "\n", "where the numerator is, precisely, the `std` index of our statistical data." ] }, { "cell_type": "code", "execution_count": 13, "id": "terminal-check", "metadata": {}, "outputs": [], "source": [ "turbIntensity = statData.loc[\"std\"]/statData.loc[\"mean\"]" ] }, { "cell_type": "code", "execution_count": 14, "id": "latest-character", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "turbIntensity.plot(title=\"Turbulence Intensity\")" ] }, { "cell_type": "markdown", "id": "009960b1-e67b-45f3-abd6-eb24a1262bd0", "metadata": {}, "source": [ "## 3. Computation of fluctuations\n", "\n", "By definition, in each point the fluctuation of velocity is \n", "\n", "$$ u' = u - \\overline{u} \\tag{2}$$" ] }, { "cell_type": "code", "execution_count": 15, "id": "liquid-monte", "metadata": {}, "outputs": [], "source": [ "turbVelFluct = turbulenceData-statData.loc[\"mean\"]" ] }, { "cell_type": "code", "execution_count": 16, "id": "coordinate-massachusetts", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "turbVelFluct.plot(subplots=True,layout=(4,5),figsize=(20,20),color=\"b\",sharey=True);" ] }, { "cell_type": "markdown", "id": "2bdcd9e6-79c3-42b7-9b26-215bba5e748b", "metadata": {}, "source": [ "## 4. Computation of turbulence kinetic energy\n", "\n", "The turbulent kinetic energy (TKE), $k$ is computed as\n", "\n", "$$ k = \\frac{1}{2}\\overline{\\boldsymbol{u'}\\cdot\\boldsymbol{u'}} = \\frac{1}{2} \\overline{u'_i u'_i} \\tag{3}$$\n", "\n", "and we should need also $v'$ and $w'$. We are then only computing the contribution of $u'$ to TKE. Note that although main flow is in the $x$ direction and components of velocities $u$ and $v$ can be neglected, it is not possible for fluctuating velocities $v'$ and $w'$. They can be as important as $u'$. We can make the assumption that turbulence, at small scales, is isotropic and, hence $\\overline{u'}^2 \\approx \\overline{v'}^2 \\approx \\overline{w'}^2 $ and\n", "\n", "$$ k \\approx \\frac{3}{2}\\overline{u'}^2 \\tag{4}$$" ] }, { "cell_type": "code", "execution_count": 17, "id": "accepting-reading", "metadata": {}, "outputs": [], "source": [ "TKE = 1.5*statData.loc[\"std\"]**2" ] }, { "cell_type": "code", "execution_count": 18, "id": "cooked-greece", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "TKE.plot()" ] }, { "cell_type": "markdown", "id": "12cfb03b-f263-43e9-bdc6-659aa7b1150d", "metadata": {}, "source": [ "## 5. Some time scales\n", "\n", "For the moment, we focus on $y = 0 \\,\\text{mm}$ time series. The TKE in this point is" ] }, { "cell_type": "code", "execution_count": 19, "id": "minimal-nursing", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.8969099438209802" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k = TKE.loc[\"y = 0mm\"]\n", "k" ] }, { "cell_type": "markdown", "id": "accomplished-whale", "metadata": {}, "source": [ "The turbulence Reynolds number, locally defined in this point, is calculated with a length scale, which can be estimated, for now, as the larger eddy in the flow, of the order of the profile's chord. \n", "\n", "$$ \\text{Re}_t = \\frac{\\sqrt{k}c}{\\nu} \\tag{5}$$\n", "\n", "We need also the viscosity of air." ] }, { "cell_type": "code", "execution_count": 20, "id": "underlying-jurisdiction", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Re_t = 24332\n" ] } ], "source": [ "nu = 1.5e-5 # m^2/s\n", "c = 0.265 # m\n", "Re_t = np.sqrt(k)*c/nu\n", "print('Re_t = {:.5g}'.format(Re_t))" ] }, { "cell_type": "markdown", "id": "adult-visitor", "metadata": {}, "source": [ "The [Kolmogorov time scale](https://en.wikipedia.org/wiki/Kolmogorov_microscales) can be estimated as\n", "\n", "$$ \\tau_k = \\sqrt{\\frac{\\nu}{\\varepsilon}} \\tag{6}$$\n", "\n", "where $\\varepsilon$ is the energy dissipation rate, that can be estimated as \n", "\n", "$$ \\varepsilon = \\frac{k^{\\frac{3}{2}}}{c} \\tag{7}$$ \n", "\n", "(it is considered that energy is injected at larger scales)" ] }, { "cell_type": "code", "execution_count": 21, "id": "fiscal-argument", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "9.858803164295557" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "epsilon = k**1.5/c\n", "epsilon # m^2/s^3" ] }, { "cell_type": "markdown", "id": "perceived-footwear", "metadata": {}, "source": [ "And the Kolmogorov time scale is, approximately," ] }, { "cell_type": "code", "execution_count": 22, "id": "quantitative-parker", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.0012334840317132266" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tau_k = np.sqrt(nu/epsilon)\n", "tau_k" ] }, { "cell_type": "markdown", "id": "bigger-fault", "metadata": {}, "source": [ "that is of the order of our time resolution." ] }, { "cell_type": "markdown", "id": "sudden-framework", "metadata": {}, "source": [ "An integral time scale is defined with the autocorrelation of time signal. \n", "\n", "$$ R(\\tau) = \\overline{u'(t)u'(t+\\tau)} \\tag{8}$$\n", "\n", "Computing autocorrelation is very time consuming, but pandas has a [plotting method](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.plotting.autocorrelation_plot.html) that performs this computation much faster. The problem is that the output is directly a plot, and it is tricky to get the autocorrelation values from it." ] }, { "cell_type": "code", "execution_count": 23, "id": "aging-kazakhstan", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "uPrime = turbVelFluct[\"y = 0mm\"].values\n", "pd.plotting.autocorrelation_plot(uPrime);" ] }, { "cell_type": "code", "execution_count": 24, "id": "remarkable-halifax", "metadata": {}, "outputs": [ { "data": { "image/png": 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H7XPnzmXmzJmUl5fz0ksvddh+yimnMG3aNIqKivy69l7Zn0BqmIew0FBvwAF48I0NjKnY1OH4vl57AB6FhedfyNi0lMP22hsxYgRg115n115/dNeQYC3wSTevI9rxw5znOS/v8L+0s6kykk2VTqvxjOhGGjwhNCvER4Wxv6SWek8Io6M7NsNevaek3+ltalYe35/AxorIfn9Wi3oPPLRy3xEzzYMqHKw/ogfD6JW9ZY0Bm/epvDGEPTURjIqoY2xM6w/YaZOH88KGIhoGeMSol/Pjyfzjx+ztpHbAHN1E1b8Bo0UkRlWPjF+nLkyYMEF/+tOfepcf3efMS3fjuDK/jn+lII5PyqK5LL2CiBDl2Tyn2mxGfD1bK51gcFFaJcsKnL47N44t5dH9SSxMreL04f2bbHVnVQRP5Trnu3v6oX59Fjglne2eNF4vjGdKbD3XjhmoaZIGXpMH/nMwjoL6MPLrwvna+FLSowbux7isrIzExEQA1pRGsfxQLOekVlPbHMKZKf5f8rXNQlSIMhD9hRs88OsdqYyNbuDGceWAc5MQGeIEiJhQD+H+tD310yP7EsmtDefCxANMS4nkyZwExkY3ctywOh7dn0RcaDOLRlRzQkLfWny296vtKTSqDMjfxmDxvS6CobwxhNgwD2GHQf/zG2644RNVnTsQn9XjZSsip4jIFpy+OojICSLyfwNx8mBLiWjmUIP/d85F9aGMiW7k+IR6Rvn86I2Oar0zTAxvHeUgOaKZcFGqmvr/61Doc4ffNEB3nbuqnXr6/Pow/Lz36FZxQwhvHIylvHEAfw2Bzyqi+LQ8mvw6p9pyT7Xz776aMNaVRQ1I2sEpSa0oiqXOE8J/DsbzTlEstc3+/cVXNoVw784UPiiJHpC0HKp3ar7310agCpsrIvjNjlSezhnGA7uTeWx/IgB1zUJZP/O73gN5tWFMi6tnUmQ18WEevj6+lAtGVjE2ponhEU1UNYfyUv4wPP3Ia1V451AMB+rCaHI/J6c2vPuDhqic2jDu3zWcdw7F9rzzEcaf1mt/AM4DlgGo6mcicuZgJmqwDB8+3FvPC9D03m7W/WcrF33hGpJje35Q+td73uHkCclc/8VZAMzJLiIhOpztBZW89c/PALjq0s/zxAPvAXDbTV/hn7/LYsToDK6/ena/0r7zpY1waD8Apy6+jGNGDevT52QXVrJmbykzq3bx2KpGoJGqplAyP/8FJqT07wK/e9lmPtq9l5nHHsu3Ljym233rGpvJ2l7IOTNGEh7a/Y/m8r99DAVF3uV3y4bx/67/PGf+dgUAN16+mFljEvuc7qysLDIzM9mQW0bN9jazeDB/0UXMHpvU82dsL4TsNXxWN5y/Xt/pNFB+aWr2ICK8uC4X9m0A4OyLvsA7/94EFLGj2ilR59WFs+DzX+CWJ9exJb+CXb++gNCQvt0Sf7KvBN3xId+77DTCCpPJzMxss31+QQW3PrWO3YeqSZ97Hucfl96n82zMLednD63i3WLnOosKD+FAUyzJs+eTGB3OmVNT+/S5g6Xlugi0Zo9y3aOrgSK21yfy9PVfCHga2rvhhhsG7LP8ukVS1Zx2q46KGdAmjYgDYNehqh73VVWKqupJiW99pnLa5BRmZiS0CVjD4yI4Y0oKZ01NRURIiYukqA/9gdrbX1JDTIRT2tl+sIK6xr79F1y19GN+9K+N3PzfGspqGrl9wWRE4F/rcns+uAcfu8+u3t9V3MOe8Pf39/L1J9fx+Ad7u93vQFktH+wqZmxyDAD3XXkCdY0eHlqx07vPB7uKujq8g7V7S3jonZ10Vq388Lu7Adr8eO8+5N8zh13ufs3tigI1DU2c/bssnlm9n5U7DvHaxvwOx+4vrvH+f/745U0c85M3+P4LG7zbP9xVzMa8ci6ZNYo/XjWLZbc701k9vXo/W/KdatHNB8q9++eX13KgzP8qq5ZWnOO7uOmYnjaM1791BhmJ0Ty0Ipus7YWd5l9P1u1v22n6mnnjqKxr4pvPfMpXHl1NZV3fRgg52vzPvzayKruI4bERFFc38D8vbeQfH+7lw13FvPhJLn9ZuWvAzvXR7mJ+9spmPP0pwvaSPyWdHBE5FVARCQe+BWwd3GQFxuRUJ+hkF1Zx0vju+7tW1TdR3+QhJa5jiSgxprWKICkmgn/cdLJ3OTUu0q+g1pN9xTVkTkvlzc0HeWZ1Dt957jP+8qUTWTzTv7vOx97fQ0q8EwDTE6LId5t6f2n+OHYWVvLIe3tYPDOtz827S6sb2Fbg/ADuOFhJbUMz0RGdV11W1DU6JQPgo90l3HzGxC4/d8X2Qpo9ymM3nMTw2EgSYsL5y8pdLPvsgHefPYequf+tHXyaU8YTN87rNp23PrWOwsp6ThqfzMkTh3vXby+o5D8b8rn+1PGU1zby0qd5AOwu6v7/rriqnjP+dwUjhzkNTMprG2ls9nhLb+v2lbG7qJof/Wuj95gPfng2oxKjvfuf+dsVzEgfxmvfPJ0X1+V5R7c4bfJwthdU8cInuZTVNDJ3fDIXz8oA4LxjR/Lwyt2teVBUzfGjE1FVLn7ofQor61nx3Uy/Sq/7i50ANTopmq5uPSLDQjl9cgrPrc3h+r+v4f4vnkB0eCip8ZHMGedfX/EcN7jNn5jMiPgovnveVMprG8krq+Gj3SV8sq+UzGkj/Pqso9WOg5X885McvjBnNF+YO4YrH/6Qpz/e32G/FdsK+fbCqZwyaTiq2ueBh69a+hEAp09O4ZwZI/uVdn/5U9L5OnAbkAHkAbPc5X4TkcUisl1EskXkh51sjxSR59ztH4vIeJ9tP3LXbxeR8/py/ozEaCLDQsgu7DkotPTHSYnr2Hos1af0ExEW0mFbf0s6jc0e8spqmZgSR1JMuLc13H82FvRwZOvxd7+yhduf/hSAHyyezvfmRvHPr59CWkIU3ztvOiECtz21rk93sKrKkx/tQxVuyZxEs0fZkl/e6b4l1Q0cf/d/vaWingLylgMVDIsKY0JKLAlucJ+WNsw7KkRGYjT7S2r44/KdvLvjULct8TwepdAd+uiDXcV8llPGqxsOuMtOaWnJmRP55SUzefuOs5iUGssHu4p5bWN+l6WplTsOUdPQ7O2j1eRR9hW3lo7W7O3YcvGznDLv+425Tj5tza8gv7yOhiYP3zh7Mn/9ylyevOlkTps8nLVu/5kTRid6j3vw6hP5f5+bwXWnjAMg1+20XFTV4P2OK7YVdpkXvvaX1JA2LIqo8O6fb540oTW4PLM6h68/uY6vP7nOr3MA5JTWMGVEHM8uOYUHrp5NTEQYv7/yBP76lbmIwHqffBlqthdUUlbTwPWPriYpJoLvnTeNueOSOGf6CK4/dTy/vGQmEWEhnDElhaSYcD7eU8KSJ9byi1e3cPzd/+XdHb1rXFRV38Qdz633Lr+3s/X6PlRZT1FVPZvyyttcywOl25KOiIQCf1TVawf6xO5n/wlYBOQCa0Rkmapu8dntJqBUVSeLyFXAvcAXReQY4Cqcka9HAW+LyFRV7VWdU0iIMDopuseqiA+yi7jmkY8Bp6qhvQz3rrVlnh5fKXGRlNa0vfvtrX3FNTR7lImpsSTFRFBU1QA49f/+yGnXCXZ0UjSJKaHe0t3kEXF8Z9FUfvmfrRRXN3QaWLtz/9s7eWD5Ts6cmsqX54/jz1m7uPzPH3Lh8ek8ePXsNndhj65q7Q9x1tRUVu44xP9lZXNrZufDruwvqWFCSmybzxib7OR3TEQox49O4PVNrcF3Y245o5NiOv2sXJ/RJLbmV/DH5U4V3QMLYthyqIKUuEhvCWTyiDguO3E0v31zO7c+5fyw7vnNBR3uKFft7BiM/rg8m7OnpxITEdZp0Nl0oNz7XOSz3DLv+g/dasnMaane0sOtmZP5dH8ZGYnRzMxovfYiwkK8JcRXN+R7g+32gkrvPqv3lHDJ7Azyy2u7LcHuL6lm7PDO88zX5SdmcFxGAve9tZ03Nx8Eeh6/sKymgSX/+IQvzx9HTkktY5I7nic+KpypI+IP6wF0V+8p4YkP9/KrS48jIbq1ZmNTXjnT0uIJDw1hxfZC7n19GxfPyuC/Wwq47pTxXDI7o8fPrqhr5Lw/tPZzeuLGeYxwS85/u/4k7/ovzXduMA6U1fL21oP85OXN/M39e/rms59y56KpXHnSGOoaPN4bNF8vr8/jjU0FXDFnNBvzyvmXW5pPjY/k/ewiVJXqhmYuemgVhZX1NHuUpJhw3r7jrD7kWNd6bDItIquAs1W1YUBP7MxMereqnucu/whAVX/js8+b7j4fikgYUACkAj/03dd3v+7OGR8fr3PmzGmzrmDGlWhIOOmbnQ5SzeExSHMjIR6nfrlo4mKqRhwHQGRFLmlbnqGzgmxjZALiaSasse2de+WI4ymeeB6jP/lzh21NEcOoSJtN0v53ka774VKdPI1DUy8ifeM/KBl3FvXDnKF1QusrSNvyHOH1Zd19baqTpnBo2iXe5YxP/0r1wb1tmoPWJozn4IwvkLb5GaIqe36+oxJCc3gsoQ2V5J54CxHVhYzY/iIC7D/xVjwRse65Hia83ql2q48dSf5xXwEgfdOT1MemUTLBeeg+7qPfdpqvecddR1h9BSN3tHZ+bMnT0IYqYou3UZHe2pIzMWcViXmdXwY1iRMpnH45IY21eMJbW5nFfPo0zZPPQjzNpG19rvU7Avvmf68139b/lfC6Mu+yJyScnDm3oqFOlWt49SE84dE0R8S1ntTTTFTFfuoSJ7j7FBLWWMXIbS8CUDj1EmqSpwAQXZJNbdIkxq75o/f688eBmdcS0tRA2rZ/UjI2k4r0OcSUZFM3bDQaEoaGRjDu4/uQTu7JFMiZcxsxpdmk7H7Tr2bCFSNne//fAMau/kOH9KqEUB87kvr40ZSOy0Q8jeBpJq5oC8P3duzkXDThXKqHT2Ps2oe6/VsIJN+8yDv+BhpjUkjeu5yoihyKJp1PWF0pNcOnE1W2l+iy3VSOPIGm6OFtPiOucANJ+7IIaa5HgKbwWDxhUUTUtj73rEmaTOG0S73L4z7+PaLd31AqUHDMVYinieT9Kzk47TKaI1tvSkIaa0k48DFRFTk0RiUS2ljNwelXQEjrjXF4zSESc96nOSKWkgmLiC3aQlNkAvVxo4g/uB5PaDjVqTMJrz5E9kMD12Tan2c6u4H3RWQZ4C1rqep9/Tx3BuDbQCEXOLmrfVS1SUTKgeHu+o/aHdvpLYWILAGWgNMLuaysrM325qpimlKnkz/yFCJ3r6TinO8RWraf+I8exhMR5w04UltG9Ad/pvNKI4CyTtc2RjjF3qLY8WhkHFHb3/T+UVXNvZSmlMl49q8jrCwHhU5/eKsmz0Dqq6g5sANP6ixn9DugOXIYecd9mYR3foN4uu63Upua2Pbzig7gaW5ukxfNjU6gqWgKoa5dHnWmbtLZ1E05h9g1jzo/stkrKHePi9jzHnXTnN7WZZ5owsucOum65BMAiPnsOWrzt+KJ2A/jMiEkjNJaDyH1HfsKNYVGI9X72qS1ib0w0enV3lB2ENzHWlJfSXVILHSR/rrhzt1+aOFWPBkntn5e3EgaYlKJyFnb4fqIXfs4tdPOwxOfRnFUBlEFe1uPSxqPhkYQte016qZfQEj+BqL3fkD9+NOon+wOxB4SStjWN4hMnUpYyR4aR82mdvQccmZcA0BzbCqhFQdoHjaK2uTJhFQdoqKkd1UlWllE/fDJHMjIpGHUSYQf+AwtzsYzfKp3n6KwVDQsgvCCzW2CT3N0Ep7wGJoP7aGsrIzmdtdFp+er+oCQlJl4ohIgPJrSxlBCK9umuXb6+dSPP731mJBwCAmnsayg08/3FGxDR55AsSeasIoDHbYHQ0teeMJjaIx2Sp6VkSMom3Q8nthUGmKdZyB1ieOpSxwPQNTOtwmpOoh4PFTP+TJVI46nasTxSGMtNNWh0U5LyNg1fye8OBuAmvTWZymhZfspL/WvM3n0B39xjgfiD9xL3fjTaUw7jtDyXJoTRlE6LrPtAZ4m4lf+jqbUaTSkH0/UppdorD6EApEaSfVEp1FyxN73Cd32GqFA9JiTqR/b/XPS3vKnpPPTztar6s/6dWKRK4DFqnqzu/xl4GRVvd1nn03uPrnu8i6cwHQ38JGqPumu/xvwuqq+0N05586dq+2H23hg+U7ue8sZImNCSqy3bn7Pby4ga/shbnjMmTrojkVT+eY5U3r9PT/dX8ql//eBd/mNb5/hraJb/Id32VZQyb2XH8emvAqWfXaAld/LbDPOVcso1l+eP45fXDKTX7y6xVukbvHC109hbhcNIeoam7nkT+9T3dBETolTvbT3ns91aA5aXFXPnF++zc8uOpbrTh3f4/f6yqOreXfHIWZmDGNTXgX/vu20Ns2WS6obOPEXb/H9xdM4PiORueOT+PG/N5G14xBr7mq9S/5kXymX//kD/vqVuSw6pu2DzGaPMuWu17htwWTuPHead73Ho3z7ufVcdMIoGpo93uqvkyck0+xRXrjl1A7prahr5Mz/XcG45BgumZ3Bz17ZQkJ0OPFRYd5qt4e/PIfzjk3r9Pte8Mf3SIwJ5+mvzveu+/v7e/jZK1v4+H/OobKukQkpcd6Wb6rKss8OcNL4ZG+VHcATH+7lJy+3HbLlV5fO5K6XnGFmrpw7mv+94oSuM74Tb205yFefcK7rhTNGcv8XT6C6vpn5v+lYorh9wWS+e56Tl8VV9SzfWsj3X9zAq984nZkZCb1qJrwpr5wLH1zVoUHL/uIazrkvi8Zm57fl/Jlp3irQJ26c12nT6ILyOub/ZjnT0+J55Rund1kVvWJbIdPS4hmVGI2q8sWlH3FM+jDuvuhYv9LcGy158dTH+7jrpU2MGx7DvmKnGvN7501jT1E1nzsunX3F1by3s4jtBytZdvvp3tasdY3N3PXSJqf5eyfmjU/mQHktuaW1LDpmJDeeNoEZ6fEDMs5ds0dZlV3EVrd141tbDnLuMSP52lmTujwmv7yWyromJqfGEdKu+b2IBKak4z53mToYz3RwGiWM8Vke7a7rbJ9ct3otASj281i/HD+6ta7bd8DOgxX17Cx06sc//fEikvzox9OZ9s9HtuVXUlTZwE+WbfI2x/3Bi60tm7ILq9oEkP9ucerO7zzXuWttaVp78+kT2JBXzuo9JRwo73q07M898B67DlVz+YmjySnputosITocEWfg0j+8vYOzpqZ22z+lxh2eZVNeBRGhIcxIbzuDalJMOFHhIfz+vzto9ij/73Mz2FdSw7h2dfoz0uMJEecHrH3QKa1pwKMd8zAkRHjA7ffk+382NjmGFdsLWbGtkNOnpLT54XpnayFlNY387bpjKa91aopHxEeSlhBFbmkts8cmsqib1jsz0oexKrvt3fy2/EqSYyMYER/pbb3WQkS8Lc18LZwxkp+8vJmbTp9AUkw4jc3KNfPGeoNOX/qqLDpmJL+4ZCaRYSFcOdf5s4iPCueb50xhc145B8rrvD8+7+08xHfPm8aKbYXeG6qYiFCmp/V+BtyW50Bb8ivJnDbC2xDhhXW5NHuUUycN54NdxVxz8ljW7ivlUGV9lyNWpyVEcduCSfxpxS7+krWLr545sUPDhuzCSm54bA2zxyby0q2nkVtay+o9JazeU8IPz5/Oy+vzKKyoZ874JBKiwwdkoN39xTX8/JUtTBkRxxdPGsMv/+M03L3xtAltWmdef9qEDsdGhYfy+ytP4JeXzOTR9/dw3rEjvY1O/rJyN5sOlDM8LoLzZ6Zx57nTmDwirsNn9FVoiHDW1FTOcq+nr3cTbFqkJ0STHoCxibsNOqraLCLjRCRioJ/p4Mw+OkVEJuAEjKuAa9rtswy4DvgQuAJ4R1XVrep7WkTuw2lIMAVY3ZdEnDY5hWtPHsvmAxWszynj5tMn8MiqPd67xFEJUX0OOOD8MfnaV1zDv9fnddn/I7e0lrnjnfcVdY28tjGfzx2f7r37ufH0CWwrqOSWzElEhIVw3N3/7bIhRFFVvbf/yC2Zk1gwPZWJKZ1f2GGhIQyLCuffnx4gr6yWJz/ax9r/t6jL77XXp1XL9PR4IsPa/kCICOkJ0d6g8Mm+UgrK6zp04oyJCGNSahyb8jpWXBZWOA+pfVsHtjd+eAyTUmP50nynz0dRVQM3PLamQ8n0o93FJESHM3tMIpX1TVw6O4NbMyfx6oZ83ttZxHfPndbh7s7XxNRYXlyXS01DEzERYby5uYDn1uZw2uThvWquOioxmve+v4C0hKhO7+bPmd63Zqtfdh8y+7pjkXOj8uRH+7j3jW3MGpPIh7uKKa9t5FvPfurdb8qIOML60MhlWFQ4STHhPLB8J//4cC+rfnA2sZFhfLSrmJkZCTx49Wxe31TAaZNS+OfXTqG+ydNtJ+zvLJzKK5/l8/u3dlBc3dCh9PK621rz0/1leDzapt/Px3tK2ty8Abx9x5lMSo3rc3NigOfW7qe+ycOD18z2tpicNSaxy+4AnYmOCG0zP9HxoxO5eFZGv5o6H8mC9kzHfUZzO/AmEAo8qqqbReTnwFpVXQb8DfiHiGQDJTiBCXe/54EtQBNwW29brrUIDw3hV5ceh6pSXN1AeGgIj7jVV8NjI7jypDE9fELPn+/ruTX7Oy2ZLL/zLM75/UpyS2u8VTO7DlVT09DMFXNGe/eblBrHiz7VR/FRYeR3EXQ2uC2jnlsyn8kj4nq8k6prbKbcncK7qKqB8trGNi11AO58/jNGDIukqKqB6WnxbCuo9Lbea290UmvQ2XWoioLyOtJnRnXY76QJyby0Lo/q+iZi3RaAj72/xzsnUXet6USE5XdmAs5w/O2/e4v1OWXMGpNISIiQEB3O/e6oErcuiGFCcy6nTU7p8hwAoxKddOeX1xETEcrX/uGMedtZa8aedNaC6+mvnkxpdWOvfsz89aX54/jS/HG8teUg7+0s4k8rsqmoa+IbZ0/mwXeyuaCPIwwA3iq00ppGnl+bw1UnjeXTnFJuPH0Cw+MivS2uuup46issNISnbj6ZM/53BU+v3s+d504lPsq5/rK2F/L7t1pHil50/8o2fZCWvtuxw+TC+97l6nlj+M1lx/fyOznBxaPKC5/kcvb0EUxPG4bHo/z4wmO46IRRvfq8rgzFgAP+BZ1d7isE6H0ZvBuq+hrwWrt1P/F5Xwd0OgaEqv4K+NVApaVl9ACAq+eNYVRCNN/owzOczvz4wmNYt7+UNT5VYSPiIymsrOerZ0xg3PBYJqXGkRIXQW5pLVnbD/GtZ9cDEBkWwllTuq5yGZUQTV5Z59Vr63PKCRH8noSr3u2U2FIHn11Y2abj34Gy2jb107efPZmPdhfztTM7L7pPT4v3tv/fcdBpude+5AdwyawMnv54P29uLuCyE0ejqix9t7Xj49hOfqQ7M29CMpFhIdQ3edr0vappaGLHwUrOPaZjKSIyLJTEqJ7v8tOGOYH1+TU53pELAE70Y4gcf5w6qfugNxBaSplL391NSlwE3zpnChfPymBSat+HP7r38uO5763thIeGsPTd3YwcFkVjs3LKxOE9H9yJMckxvHzbaVz8p/e5/u9reODq2SzfepDfvLaNuMgwHrvhJLYfrOTuZZvZdaia0yenkFdWy/vZxYSHCu99/2yGRYdxqLKeP769k2dW5zA6KYaLThjFyGFRHfrR+SqvbWRDbhnfenY9cZFhnJ3exMGKBn52kXPTFxIi3HR6x2o00zu9GWU6DkBV+9+9PkjajzIdaDurwnkqN4HPjaxiRnw9myqiODmp1jsq8V/3JhIZoqRENLO6zPmRGxnZxC0TSrv8zKdyhrGzOpIZcfV8cXTb1l9P5iRQ0RTCrZ0c31nT2HVlUawujeKKjEoe2p3MJekVzPIZVXhbZYR3ZG2AOyYVMyy866adB+tDWVUcQ1yYhw9LnMBxZUY5x8S3ran1KPxhVzIVTaHcMLaM2DAPD+1OJi2ykSlxDZyT6v9Iz80KK4tieLc4lq+PLyEx3MOf9yRR3hTKNaPLmRrXsZbYn2bCxQ0hPLi77Q/p5aMqmBlfPyCjSgfKfdlOPp+cVMP5IztW8fZ1ZOX9NWE8tj8RD0JEiIc7JxcT2Y9xSN8tiiGrKAaPT3vOs1OqvaN+76sJ451DscxPriW3Npz3S2KYm1jLhWmtP09VTcLvsp1gHiqKKsxJrGNKXAO1zcLasmiuGV1ORIhS2yw8kZNIYX3b+/ARkU0sGV96WIz0HEwDOcp0jyUdEZkJ/ANIdpeLgK+oasdZk0y3psQ1cvf01s6E85PbVoslhjeTXxdGdXPrX+uIyO6H8B8d3cTO6ki2VkVSVB9KSmQz1U1Cfn0YubVhzIj3fzSEExPrODGxDrfqmorGUDwK75dEk1UUy8SY1h/syBBPtwEHYGRkM5ePqmRPdbg36AwL63hMiMDk2AbWlUfzdO4wFrg/LFdmVJAc0bshtUMFRkQ6Na1/2esEzvKmUGcE5di+P5b0Tfe46AY+n1ZFSuSRNwThSUm1rCqOYU5i76dq787YmCa+PKac/xyM4/ThNf0KOABnptSQEN7Mv/PjOSW5lpOTatv+H8Q0cYM75cPk2AbSopqYEdf2Wo8LU67KKOetQ7EUNzg/dWvKollT1lodfO/OFCJDPNR7nATHhHq4KqOcdeVRNDQ0cMmYhiEfcAaaP9VrS4E7VHUFgIhkAn8FOrZLPQIdTrM3vvXEe2yudP5LpsXVU9wQyi0Lj+WCedO7nDn07qtO55Tdtfz6tW1sqozkrIgaHtufyCH3j2zxvBlcf86xnc7eCHQ6c2h4iPPHV94UwriTFvLzJ50RtHdWRxIb6mFSbAOnJjuBwZ/ZG+sam3n8x86sqAk+Uz/4zt444u0svrm8Co8Ku2vCSQ5vYnRiVJ9mDp3oE1w2N48iJqKWW44Pp6xd94eW2RuzsrIoKSnpcfbGFlPjGkiJbA767I19ufbOGF7LGe78NQM9a+2E2EZun9haqu5u5lDo/Nrz9auvXsyvwyLZtnkDn332WYftvtdeeDczh85/6z1+vaqEmfH1bKqM9JZmPnd8Ov/ZkO8NOAC3TCglPszD9BQPI0aMIjMz02YODeDMoS1iWwIOgKpmAUffJA+HAd+5eBamVnP7xFKOS+8+qyPDQlhy5iROSI9hS2UkmyojvQEH4KSxfWsDmRjezCdl0dzzX6cDW0vDroyoRi4bVUlalP93+VHhoYwbFkp8WDPxYZ1X58aGC4tHVNGowo6qSEZ1MgOrv2JClTsnO3/kOwurOGtqKqEDeLc6OtpGQw6U6IjQfj9wHxEbyq0TSjkzpYZbJ5SSHtlIVIhy7+XH89TNJ3N6Rhg3ji3ly2PKiO+kJG4Glj+dQ18C1uFUsQF8CZijqpd2fdThqbPOoYeTyrpGfvnqVhYdM5KFnTz07s69b2zjr+/uJiREiAwN4fVvn0Fdo6fLFms9dQL80iMfsyrbqQqcNyGZUycN5w9v7+SbZ0/mDp+Omv5q6V/U3aCS72cXca07xt0PFk/nlsye+xZ05zevbeXpj/fzxE3zuu1z5G+HyPv+u50H3slm2y8W9zg45pEqWHPIBFJdYzNV9U09jjE4FPLCXwHrHOq6EfgZ8C+cIX/ec9eZARYfFc69V/SueWeLsckxNHkUPMqPzp/e5aCX/rr7omN5a8tBhsdGcMKYREYnRVNd38S1nfQH8Yc/P9Kjk1rr2tt3Nu2LH10wg++dN61PfVA6851FU7l1weSjNuAMFVHhofZ/GEQ9Bh1VLQW+GYC0mH6Y4lOi6arfTG901q/nrs91Pxtof6UntKb7mPS+zYza3kAFHHCa1duPlTH90+NfpIi8JSKJPstJ7qjO5jDiW300MXXghtMIJN8+FN2NQmCMOXL5U72WoqplLQuqWioiQ3t6v8NQaIhwyaxRvLOtsF+d/YLtwatnU1rTMGR7axtztPMn6HhEZKyq7gcQkXFwmEx4Ydq478pZNB/h4zl9foCGGDHGHJ78CTp3AatEZCXOdC9n4M5PYw4vISFCSKcz8hhjzOHBn4YEb4jIiUDLRCLfVtXOJ4w3xhhjuuFPSQec0QfO9Fnu2LXeGGOM6YE/rdfuAb6FM43AFuBbIvLrwU6YMcaYo48/JZ0LgFmq6gEQkceBT4H/GcyEGWOMOfr423Mu0ed9ACY0NcYYczTyp6TzG+BTEVmB03rtTOBHg5oqY4wxRyV/Wq89IyJZwEnuqh+oakE3hxhjjDGd8qchwXJVzVfVZe6rQEQ6Tq7RCyKS7A6vs9P9t8MQwCIyS0Q+FJHNIrJBRL7os+0xEdkjIuvd16z+pMcYY0xgdBl0RCRKRJKBFHe8tWT3NR7I6Od5fwgsV9UpwHJ3ub0anBlKjwUWA3/wHQMO+J6qznJf6/uZHmOMMQHQXfXa14BvA6Nw5tNpUQE81M/zXgxkuu8fB7KAH/juoKo7fN4fEJFCIBUo6+e5jTHGBIk/k7h9Q1UfHNCTipSpaqL7XoDSluUu9p+HE5yOVVWPiDwGnALU45aUVLW+i2OX4A7bM3LkyDnPPvvsAH6TI1dVVRVxcUfmaNQDzfKileVFK8uLVgsWLBiwSdz8CTpf6Wy9qj7Rw3FvA2mdbLoLeNw3yIhIqap2OrWjiKTjlISuU9WPfNYVABHAUmCXqv682y/C4T9zaCDZrIitLC9aWV60srxoFeiZQ0/yeR8FnINT3dZt0FHVhV1tE5GDIpKuqvluACnsYr9hwH+Au1oCjvvZ+e7behH5O/BdP76HMcaYIPOnyfQ3fJfdh/n9raNaBlwH3OP++3L7HUQkAngJeEJVX2i3rSVgCXAJsKmf6THGGBMAfZnLtxqY2M/z3gMsEpGdwEJ3GRGZKyKPuPtcidMR9fpOmkY/JSIbgY1ACvDLfqbHGGNMAPRY0hGRV2idtC0UmAE835+TqmoxTjVd+/VrgZvd908CT3Zx/Nn9Ob8xxpjg8OeZzu983jfhBJ4vdrGvMcYY0yV/numsFJHZwDXAF4A9wIuDnTBjjDFHny6DjohMBa52X0XAczhNrBcEKG3GGGOOMt2VdLYB7wEXqmo2gIh8JyCpMsYYc1TqrvXaZUA+sEJE/ioi5+BMbWCMMcb0SZdBR1X/rapXAdOBFTjjsI0QkT+LyLkBSp8xxpijSI/9dFS1WlWfVtXPA6Nxpqr+QQ+HGWOMMR30qnOoqpaq6lJV7dDHxhhjjOlJX0YkMMYYY/rEgo4xxpiAsaBjjDEmYCzoGGOMCRgLOsYYYwLGgo4xxpiAsaBjjDEmYCzoGGOMCRgLOsYYYwLGgo4xxpiACUrQEZFkEXlLRHa6/yZ1sV+ziKx3X8t81k8QkY9FJFtEnhORiMCl3hhjTF8Fq6TzQ2C5qk4BlrvLnalV1Vnu6yKf9fcC96vqZKAUuGlwk2uMMWYgBCvoXAw87r5/HLjE3wNFRICzgRf6crwxxpjgEVUN/ElFylQ10X0vQGnLcrv9moD1QBNwj6r+W0RSgI/cUg4iMgZ4XVVndnGuJcASgJEjR8559tlnB/4LHYGqqqqIi4sLdjIOC5YXrSwvWlletFqwYMEnqjp3ID6ru+mq+0VE3gbSOtl0l++CqqqIdBX5xqlqnohMBN4RkY1AeW/SoapLgaUAc+fO1czMzN4cftTKysrC8sJhedHK8qKV5cXgGLSgo6oLu9omIgdFJF1V80UkHSjs4jPy3H93i0gWMBt4EUgUkTBVbcKZWC5vwL+AMcaYAResZzrLgOvc99cBL7ffQUSSRCTSfZ8CnAZsUac+cAVwRXfHG2OMOfwEK+jcAywSkZ3AQncZEZkrIo+4+8wA1orIZzhB5h5V3eJu+wFwh4hkA8OBvwU09cYYY/pk0KrXuqOqxUCHKa9VdS1ws/v+A+C4Lo7fDcwbzDQaY4wZeDYigTHGmICxoGOMMSZgLOgYY4wJGAs6xhhjAsaCjjHGmICxoGOMMSZgLOgYY4wJGAs6xhhjAsaCjjHGmICxoGOMMSZgLOgYY4wJGAs6xhhjAsaCjjHGmICxoGOMMSZgLOgYY4wJGAs6xhhjAsaCjjHGmICxoGOMMSZgghJ0RCRZRN4SkZ3uv0md7LNARNb7vOpE5BJ322Missdn26xAfwdjjDG9F6ySzg+B5ao6BVjuLrehqitUdZaqzgLOBmqA//rs8r2W7aq6PgBpNsYY00/BCjoXA4+77x8HLulh/yuA11W1ZjATZYwxZnAFK+iMVNV8930BMLKH/a8Cnmm37lciskFE7heRyAFPoTHGmAEnqjo4HyzyNpDWyaa7gMdVNdFn31JV7fBcx92WDmwARqlqo8+6AiACWArsUtWfd3H8EmAJwMiRI+c8++yzff5OR5Oqqiri4uKCnYzDguVFK8uLVpYXrRYsWPCJqs4diM8KG4gP6YyqLuxqm4gcFJF0Vc13A0hhNx91JfBSS8BxP7ullFQvIn8HvttNOpbiBCbmzp2rmZmZvfgWR6+srCwsLxyWF60sL1pZXgyOYFWvLQOuc99fB7zczb5X065qzQ1UiIjgPA/aNPBJNMYYM9CCFXTuARaJyE5gobuMiMwVkUdadhKR8cAYYGW7458SkY3ARiAF+GUgEm2MMaZ/Bq16rTuqWgyc08n6tcDNPst7gYxO9jt7MNNnjDFmcNiIBMYYYwLGgo4xxpiAsaBjjDEmYCzoGGOMCRgLOsYYYwLGgo4xxpiAsaBjjDEmYCzoGGOMCRgLOsYYYwLGgo4xxpiAsaBjjDEmYCzoGGOMCRgLOsYYYwLGgo4xxpiAsaBjjDEmYCzoGGOMCRgLOsYYYwLGgo4xxpiAsaBjjDEmYIISdETkCyKyWUQ8IjK3m/0Wi8h2EckWkR/6rJ8gIh+7658TkYjApNwYY0x/BKukswm4DHi3qx1EJBT4E3A+cAxwtYgc426+F7hfVScDpcBNg5tcY4wxAyEoQUdVt6rq9h52mwdkq+puVW0AngUuFhEBzgZecPd7HLhk0BJrjDFmwIQFOwHdyAByfJZzgZOB4UCZqjb5rM/o6kNEZAmwxF2sEpGegt1QkQIUBTsRhwnLi1aWF60sL1pNG6gPGrSgIyJvA2mdbLpLVV8erPO2p6pLgaWBOt+RQkTWqmqXz9OGEsuLVpYXrSwvWonI2oH6rEELOqq6sJ8fkQeM8Vke7a4rBhJFJMwt7bSsN8YYc5g7nJtMrwGmuC3VIoCrgGWqqsAK4Ap3v+uAgJWcjDHG9F2wmkxfKiK5wCnAf0TkTXf9KBF5DcAtxdwOvAlsBZ5X1c3uR/wAuENEsnGe8fwt0N/hKGBVjq0sL1pZXrSyvGg1YHkhTsHBGGOMGXyHc/WaMcaYo4wFHWOMMQFjQecoJCJjRGSFiGxxhxv6lrs+WUTeEpGd7r9J7noRkQfcYYU2iMiJwf0GA09EQkXkUxF51V3udCglEYl0l7Pd7eODmvABJiKJIvKCiGwTka0icspQvS5E5Dvu38cmEXlGRKKGynUhIo+KSKGIbPJZ1+vrQESuc/ffKSLX+XNuCzpHpybgTlU9BpgP3OYOIfRDYLmqTgGWu8vgDDU0xX0tAf4c+CQPum/hNEhp0dVQSjcBpe76+939jiZ/BN5Q1enACTh5MuSuCxHJAL4JzFXVmUAoTgvZoXJdPAYsbreuV9eBiCQDP8XptD8P+GlLoOqWqtrrKH/hNClfBGwH0t116cB29/3DwNU++3v3OxpeOH25luMMn/QqIDg9zcPc7acAb7rv3wROcd+HuftJsL/DAOVDArCn/fcZitcFrSOeJLv/z68C5w2l6wIYD2zq63UAXA087LO+zX5dvaykc5RzqwFmAx8DI1U1391UAIx033c25FCXQwsdgf4AfB/wuMvdDaXkzQt3e7m7/9FgAnAI+Ltb1fiIiMQyBK8LVc0DfgfsB/Jx/p8/YWheFy16ex306fqwoHMUE5E44EXg26pa4btNnVuTo769vIhcCBSq6ifBTsthIAw4Efizqs4GqmmtQgGG1HWRBFyME4hHAbF0rG4asgbzOrCgc5QSkXCcgPOUqv7LXX1QRNLd7elAobu+qyGHjganAReJyF6ckcrPxnmukSgiLcNA+X5fb1642xNwhl46GuQCuar6sbv8Ak4QGorXxUJgj6oeUtVG4F8418pQvC5a9PY66NP1YUHnKCQigjNKw1ZVvc9n0zKcYYOg7fBBy4CvuK1U5gPlPsXsI5qq/khVR6vqeJwHxe+o6rV0PZSSbx5d4e5/VNz5q2oBkCMiLSMGnwNsYQheFzjVavNFJMb9e2nJiyF3Xfjo7XXwJnCuiCS5Jcdz3XXdC/bDLHsNygPC03GKxhuA9e7rApw66OXATuBtINndX3AmzNsFbMRp0RP07zEI+ZIJvOq+nwisBrKBfwKR7voodznb3T4x2Oke4DyYBax1r41/A0lD9boAfgZsw5lU8h9A5FC5LoBncJ5lNeKUgG/qy3UA3OjmSTZwgz/ntmFwjDHGBIxVrxljjAkYCzrGGGMCxoKOMcaYgLGgY4wxJmAs6BhjjAkYCzrGBICIVAU7DcYcDizoGGOMCRgLOsYEiYh83p2b5VMReVtERrrrU935TDa7g3LuE5GUYKfXmIFgQceY4FkFzFdn8M1ncUbCBmeOkndU9Vic8dHGBil9xgy4sJ53McYMktHAc+7gihE4c92AM4zRpQCq+oaIlAYpfcYMOCvpGBM8DwIPqepxwNdwxvcy5qhmQceY4EmgdSh43/nl3weuBBCRc3EG5TTmqGADfhoTACLiAQ74rLoPZ9Te+4FS4B3gJFXNFJEROKMAjwQ+BC4ExqtqfWBTbczAs6BjzGFGRCKBZlVtEpFTcGb6nBXkZBkzIKwhgTGHn7HA8yISAjQAXw1yeowZMFbSMcYYEzDWkMAYY0zAWNAxxhgTMBZ0jDHGBIwFHWOMMQFjQccYY0zA/H+fWpWVuI62fAAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "autocorr = pd.plotting.autocorrelation_plot(uPrime).get_lines()[5].get_xydata()" ] }, { "cell_type": "markdown", "id": "native-cabinet", "metadata": {}, "source": [ "We change the \"lag\" $x$ numbers with time lag, form the Data Frame" ] }, { "cell_type": "code", "execution_count": 25, "id": "editorial-branch", "metadata": {}, "outputs": [], "source": [ "autocorr[:,0]=turbVelFluct.index.values" ] }, { "cell_type": "markdown", "id": "promising-retail", "metadata": {}, "source": [ "And also zoom for a narrower $x$ span. Note that the pandas function gives the normalized correlation $\\rho(\\tau)=\\frac{R(\\tau)}{R(0)} $." ] }, { "cell_type": "code", "execution_count": 26, "id": "commercial-edward", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "plt.plot(autocorr[:,0],autocorr[:,1],'o-')\n", "ax = plt.gca()\n", "ax.set_xlim(0,0.2)\n", "ax.set_ylabel(r\"$R(\\tau)$\")\n", "ax.set_xlabel(r\"\\tau\")\n", "ax.set_title(\"Autocorrelation for y = 0 mm\");" ] }, { "cell_type": "markdown", "id": "touched-binding", "metadata": {}, "source": [ "The integral time scale is defined as the integral of autocorrelation function" ] }, { "cell_type": "code", "execution_count": 27, "id": "a20f5fe0-95db-46d5-bf07-d65f8a9ebb1b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-0.0009022706750520157" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy import integrate\n", "T = integrate.trapezoid(autocorr[:,1],autocorr[:,0])\n", "T" ] }, { "cell_type": "markdown", "id": "numerical-diamond", "metadata": {}, "source": [ "It gives a very small (negative) value because the number of samples (1000) is still very low to get a good autocorrelation for large lag. It is assumed that after the second or third root, the autocorrelation is zero. So, we change the limits of integration:" ] }, { "cell_type": "code", "execution_count": 28, "id": "bf3242b5-5978-4c44-9bf3-07fc43879fbe", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.0038772428514055016" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T = integrate.trapezoid(autocorr[0:50,1],autocorr[0:50,0])\n", "T" ] }, { "cell_type": "markdown", "id": "killing-juice", "metadata": {}, "source": [ "This method has the inconvenient that there is not the lag 0. It should be included in the very first point.\n", "\n", "Alternatively, the statistic models package provides a better way to estimate autocorrelation, even with the option of choosing the number of lags for the computation." ] }, { "cell_type": "code", "execution_count": 29, "id": "edccb2dd-a8d3-469f-be80-6547e47e39fb", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 1.00000000e+00, 8.04541350e-01, 5.73932067e-01, 4.34197820e-01,\n", " 3.66033657e-01, 3.52249759e-01, 3.37537587e-01, 3.17333281e-01,\n", " 3.02811025e-01, 2.88497039e-01, 2.57130409e-01, 1.92849680e-01,\n", " 1.36546784e-01, 1.03957571e-01, 8.32353264e-02, 8.38373665e-02,\n", " 7.86032962e-02, 6.10277646e-02, 4.65580669e-02, 1.99746693e-02,\n", " -9.26964982e-03, -2.42545223e-02, -2.72775430e-02, -1.88646766e-02,\n", " -9.32923832e-03, -1.87112884e-02, -2.96367351e-02, -3.06195932e-02,\n", " -2.30782249e-02, -1.88316863e-02, -1.35537818e-02, -3.97915265e-03,\n", " -1.47696686e-02, -3.43907404e-02, -4.63080674e-02, -4.27395164e-02,\n", " -3.48795246e-02, -3.31582168e-02, -3.40160661e-02, -3.72166240e-02,\n", " -3.81736376e-02, -2.71323604e-02, -7.79263410e-03, 2.27309238e-03,\n", " 5.12746823e-04, -1.00859193e-02, -1.05058317e-02, 9.75072762e-03,\n", " 1.29933159e-02, 7.25182676e-03, 8.90439779e-03])" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import statsmodels.api as sm\n", "rho = sm.tsa.acf(uPrime,nlags=50,fft=False)\n", "rho" ] }, { "cell_type": "code", "execution_count": 30, "id": "99c45195-7d6c-4125-b111-85b3a1b9a475", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import statsmodels.graphics.api as smg\n", "smg.tsa.plot_acf(uPrime,lags=200,fft=False)" ] }, { "cell_type": "markdown", "id": "superb-patrol", "metadata": {}, "source": [ "The computation of the integral time is more accurate because of the 0-lag point." ] }, { "cell_type": "code", "execution_count": 31, "id": "promising-capability", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.004771435414182847" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T = integrate.trapezoid(rho[0:50],autocorr[0:50,0])\n", "T" ] }, { "cell_type": "markdown", "id": "346268e0-9007-4dda-898b-4e0cf16fac4b", "metadata": {}, "source": [ "## 6. Histogram and PDF\n", "\n", "PDF is the Probability Density Function. It defines the probability of an event between to values. For example, if the pdf of our velocity fluctuation is $f(x)$, then the probability that a value of the fluctuation lies between $u'_1$ and $u'_2$ is \n", "\n", "$$ P\\left(u'_1 < u' < u'_2\\right) = \\int_{u'_1}^{u'_2} f(x) \\text{d}x \\tag{9}$$ " ] }, { "cell_type": "code", "execution_count": 32, "id": "9304aa72-b61f-4c9f-a408-c7fc775388c5", "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD4CAYAAAD8Zh1EAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAQ00lEQVR4nO3dfYxdeV3H8ffHrnWjIJjsEE1bmEaLpgEiOhQSEkEeTHFJawKa7gbCRrAxoboIPhQxm2b9p0DCQ2ITqSsJUdayrk+jW1JR8B8jpLOwENt1sdbKttEwPGTRP5al8PWPuS230ztzTztn5s785v1Kmtxzzq/nfnuy+eS333PO76aqkCRtfN8z6QIkSf0w0CWpEQa6JDXCQJekRhjoktSIWyb1xbfddltNT09P6uslaUN6+OGHv1JVU6OOTSzQp6enmZubm9TXS9KGlOS/ljpmy0WSGmGgS1IjDHRJaoSBLkmNMNAlqREGuiQ1wkCXpEYY6JLUCANdkhrR6U3RJHuBDwJbgPuq6uii4+8Hfnaw+f3As6rqmT3WKW0q04cfuvr5wtHbJ1iJNpKxgZ5kC3AMeDVwETidZLaqzl4ZU1W/MTT+14AXrkKtkqRldGm57AHOVdX5qnoKOAHsX2b8HcCf9VGcJKm7LoG+DXh8aPviYN91kjwH2Al8conjB5PMJZmbn5+/0VolScvo+6boAeDBqvr2qINVdbyqZqpqZmpq5OqPkqSb1CXQLwE7hra3D/aNcgDbLZI0EV0C/TSwK8nOJFtZCO3ZxYOS/ATwQ8C/9FuiJKmLsYFeVZeBQ8Ap4FHggao6k+TeJPuGhh4ATlRVrU6pkqTldHoOvapOAicX7btn0faR/sqSJN0o3xSVpEYY6JLUCANdkhphoEtSIwx0SWqEgS5JjTDQJakRBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqhIEuSY0w0CWpEQa6JDXCQJekRhjoktQIA12SGmGgS1IjOgV6kr1JHktyLsnhJcb8UpKzSc4kub/fMiVJ49wybkCSLcAx4NXAReB0ktmqOjs0ZhfwTuClVfX1JM9arYIlSaN1maHvAc5V1fmqego4AexfNOZXgGNV9XWAqvpyv2VKksbpEujbgMeHti8O9g17LvDcJP+c5NNJ9o46UZKDSeaSzM3Pz99cxZKkkfq6KXoLsAt4OXAH8EdJnrl4UFUdr6qZqpqZmprq6aslSdAt0C8BO4a2tw/2DbsIzFbVt6rqP4EvshDwkqQ10iXQTwO7kuxMshU4AMwuGvPXLMzOSXIbCy2Y8/2VKUkaZ2ygV9Vl4BBwCngUeKCqziS5N8m+wbBTwFeTnAU+BfxWVX11tYqWJF1v7GOLAFV1Eji5aN89Q58LePvgjyRpAnxTVJIaYaBLUiMMdElqRKceuqTVM334oaufLxy9fYKVaKNzhi5JjTDQJakRBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdGmdmz780DXPqnc9ps3HQJekRhjoktQIA12SGmGgS1IjDHRJaoSBLkmNMNAlqREGuiQ1olOgJ9mb5LEk55IcHnH8riTzSR4Z/HlL/6VKbbjZl4F8iUjjjP3FoiRbgGPAq4GLwOkks1V1dtHQj1XVoVWoUZLUQZcZ+h7gXFWdr6qngBPA/tUtS9oAjjxj4Y+0TnQJ9G3A40PbFwf7Fntdki8keTDJjlEnSnIwyVySufn5+ZsoV5K0lL5uiv4tMF1VLwA+AXxk1KCqOl5VM1U1MzU11dNXS5KgW6BfAoZn3NsH+66qqq9W1TcHm/cBP91PeZKkrroE+mlgV5KdSbYCB4DZ4QFJfmRocx/waH8lSpK6GPuUS1VdTnIIOAVsAT5cVWeS3AvMVdUs8OtJ9gGXga8Bd61izZKkEcYGOkBVnQROLtp3z9DndwLv7Lc0SdKN8E1RSWqEgS5JjTDQJakRBrrUGNd82bwMdElqRKenXKQNa3itlSNPTK4OaQ04Q5ekRjhDl3o23L++cPT2CVaizcYZuiQ1wkCXpEYY6JLUCANdkhphoEtSIwx0SWqEgS5JjTDQJakRvlgkNcDFuAQGurRya7BezIVb7xzack0ajWbLRZIaYaBLUiM6tVyS7AU+CGwB7quqo0uMex3wIPCiqprrrUqpQaP63n32wq+cywXCNo+xgZ5kC3AMeDVwETidZLaqzi4a93TgbuAzq1GotKpcN10N6NJy2QOcq6rzVfUUcALYP2Lc7wPvBp7ssT5JUkddAn0b8PjQ9sXBvquS/BSwo6p8dkqSJmTFN0WTfA/wPuAdHcYeTDKXZG5+fn6lXy1JGtIl0C8BO4a2tw/2XfF04HnAPyW5ALwEmE0ys/hEVXW8qmaqamZqaurmq5YkXadLoJ8GdiXZmWQrcACYvXKwqp6oqtuqarqqpoFPA/t8ykWS1tbYQK+qy8Ah4BTwKPBAVZ1Jcm+SfatdoCSpm07PoVfVSeDkon33LDH25SsvS2qLa61oLfimqCQ1wkCXpEYY6JLUCANdkhphoEsTcOHWOxetcS6tnIEuSY0w0CWpEQa6JDXCQJdW25Fn2C/XmjDQJakRBrokNaLTWi6SrjV9+CEu3Dp6/3ozXJO/L9o2A11tGv6N0FU476gwlybNloskNcJAl6RGGOiS1Ah76NrcVqvX3tHw8+nTT96/6t935QapN0fb5AxdkhphoEtSI2y5aGO50iI58sTKz7GKrrZSjtz431mL1ova1CnQk+wFPghsAe6rqqOLjv8q8Fbg28D/AQer6mzPtUpifb68pPVhbMslyRbgGPAaYDdwR5Ldi4bdX1XPr6qfBN4DvK/vQiVJy+vSQ98DnKuq81X1FHAC2D88oKq+MbT5A0D1V6IkqYsuLZdtwOND2xeBFy8elOStwNuBrcAreqlO6tM6ekRxLb/Pnvzm0dtTLlV1rKp+FPgd4PdGjUlyMMlckrn5+fm+vlqSRLdAvwTsGNrePti3lBPAL4w6UFXHq2qmqmampqY6FylJGq9LoJ8GdiXZmWQrcACYHR6QZNfQ5u3Av/dXoiSpi7E99Kq6nOQQcIqFxxY/XFVnktwLzFXVLHAoyauAbwFfB960mkVLa25C/Xd/uk43otNz6FV1Eji5aN89Q5/v7rkuSavIH71ok6/+S1IjDHRJaoRruUgNGdVzX+slejU5ztAlqREGuiQ1wkCXpEbYQ5d61Mdz413PcTO9cdd3aZszdGmM1tcfnz78UPP/xs3CQJekRhjoktQIe+jSUgbrt1y4dcJ1SB05Q5cE2EtvgYEuSY0w0CWpEfbQpcUm/Nuj0s1yhi5JjTDQJakRBrokNcIeutSAlawh4/ou7XCGLkmN6BToSfYmeSzJuSSHRxx/e5KzSb6Q5B+TPKf/UiVJyxkb6Em2AMeA1wC7gTuS7F407HPATFW9AHgQeE/fhUqSltelh74HOFdV5wGSnAD2A2evDKiqTw2N/zTwhj6L1CY36rnw4X1Hnlh6XIP6WHNdberSctkGPD60fXGwbylvBj6+kqIkSTeu16dckrwBmAFetsTxg8BBgGc/+9l9frUkbXpdZuiXgB1D29sH+66R5FXAu4B9VfXNUSeqquNVNVNVM1NTUzdTryRpCV0C/TSwK8nOJFuBA8Ds8IAkLwQ+xEKYf7n/MiVJ44wN9Kq6DBwCTgGPAg9U1Zkk9ybZNxj2XuBpwJ8neSTJ7BKnkyStkk499Ko6CZxctO+eoc+v6rkubWLDP7Jw4ejtE6xE2lh8U1SSGuFaLtr4Nsnz59I4ztAlqREGutY1f7RY6s5Al6RG2EOXBAytEXOE766Ps5Qr9y3GjdOacoYuSY0w0CUtafrwQ97H2EAMdElqhD10Scu6cOud3frqV4xaq15rwhm6JDXCGbrWDXu10so4Q5ekRjhDV/9W0EMd/r3M6Sfv76siTYrPq68pZ+iS1AgDXZIaYctF0nW8Qb0xGehaXfZQ16XhexU3c3wk16WfOFsuktQIA12SGmGgS+rEhbrWv0499CR7gQ8CW4D7quroouM/A3wAeAFwoKoe7LlOtcg1PzY+++brytgZepItwDHgNcBu4I4kuxcN+xJwF+CbIJI0IV1m6HuAc1V1HiDJCWA/cPbKgKq6MDj2nVWoUZLUQZce+jbg8aHti4N9NyzJwSRzSebm5+dv5hRaZfZJpY1rTZ9Dr6rjwHGAmZmZWsvvlrQy1/zmqNalLjP0S8COoe3tg32SpHWkS6CfBnYl2ZlkK3AAmF3dsiRJN2psoFfVZeAQcAp4FHigqs4kuTfJPoAkL0pyEfhF4ENJzqxm0ZKk63XqoVfVSeDkon33DH0+zUIrRhvRNc8Sr8GTp6OeXT7yDC7ceu2um1pPRBvHyP8OfB9hJXxTVJIaYaBLUiNcPrdBw8+RXzh6+9hxi1sdq2n68ENr+n3SZmKga20M+qWG+Sbluj1rwpaLJDXCQJekRthyGeNqn3mZXvRm0XWNF9sq0mQY6Brvav9z+WfUfW5cKzau1+5v1C7LloskNcJAl6RG2HLZYNaqp3/Ns+z2xKUNwUBv2IVb7/zu2tX2HLVe9P07pK4Jc5UtF0lqhIEuSY0w0CWpERuyh9518am1MuqFmxuta7XOMepYH9fsyjPn00+uwfrp2txW0nNfT2vIrEEtztAlqREGuiQ1wkCXpEZsyB56H5brN3ftMXddrKqr4bVQpp+8f8mXiBY/X77woxF3Xn0BaLm+9jV/d5m1WUaty9J1n9SL5XrnN9NXX/Z8T1w/btI995vQaYaeZG+Sx5KcS3J4xPHvS/KxwfHPJJnuvVJJ0rLGBnqSLcAx4DXAbuCOJLsXDXsz8PWq+jHg/cC7+y5UkrS8LjP0PcC5qjpfVU8BJ4D9i8bsBz4y+Pwg8Mok6a9MSdI4qarlBySvB/ZW1VsG228EXlxVh4bG/OtgzMXB9n8Mxnxl0bkOAgcHmz8OPNbXP2RCbgO+MnbU5uH1uJbX43pek2vdzPV4TlVNjTqwpjdFq+o4cHwtv3M1JZmrqplJ17FeeD2u5fW4ntfkWn1fjy4tl0vAjqHt7YN9I8ckuQV4BvDVPgqUJHXTJdBPA7uS7EyyFTgAzC4aMwu8afD59cAna1wvR5LUq7Etl6q6nOQQcArYAny4qs4kuReYq6pZ4I+BP0lyDvgaC6G/GTTTPuqJ1+NaXo/reU2u1ev1GHtTVJK0MfjqvyQ1wkCXpEYY6D1I8o4kleS2SdcyaUnem+TfknwhyV8leeaka5qEcctlbCZJdiT5VJKzSc4kuXvSNa0XSbYk+VySv+vjfAb6CiXZAfwc8KVJ17JOfAJ4XlW9APgi8M4J17PmOi6XsZlcBt5RVbuBlwBv3eTXY9jdwKN9ncxAX7n3A78NeHcZqKq/r6rLg81Ps/DewmbTZbmMTaOq/ruqPjv4/L8sBNi2yVY1eUm2A7cD9/V1TgN9BZLsBy5V1ecnXcs69cvAxyddxARsAx4f2r6IAQbAYCXWFwKfmXAp68EHWJgMfqevE27a9dC7SvIPwA+POPQu4HdZaLdsKstdk6r6m8GYd7Hwv9ofXcvatH4leRrwF8Dbquobk65nkpK8FvhyVT2c5OV9nddAH6OqXjVqf5LnAzuBzw8WltwOfDbJnqr6nzUscc0tdU2uSHIX8FrglZv0jeEuy2VsKkm+l4Uw/2hV/eWk61kHXgrsS/LzwK3ADyb506p6w0pO6otFPUlyAZhZvMLkZpNkL/A+4GVVNT/peiZhsJ7RF4FXshDkp4E7q+rMRAubkMFS2h8BvlZVb5twOevOYIb+m1X12pWeyx66+vYHwNOBTyR5JMkfTrqgtTa4KXxluYxHgQc2a5gPvBR4I/CKwX8TjwxmpuqZM3RJaoQzdElqhIEuSY0w0CWpEQa6JDXCQJekRhjoktQIA12SGvH/E6GVDQLhvdUAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import scipy.stats as stats\n", "X = stats.norm(0,statData[\"y = 0mm\"].loc[\"std\"])\n", "X_samples= X.rvs(1000)\n", "F, bins, patches = plt.hist(uPrime,bins=100,density=True) # Integral = 1\n", "plt.hist(X_samples,bins=100,density=True);" ] }, { "cell_type": "markdown", "id": "abstract-tuning", "metadata": {}, "source": [ "Since we have included the option `density=True`, the integral (moment of order 0) of this PDF is 1.\n", "\n", "$$ M_0 = \\int_{-\\infty}^{+\\infty} f(u') \\text{d}u' = 1 \\tag{10}$$" ] }, { "cell_type": "code", "execution_count": 33, "id": "0d878855-1f8a-4410-898f-5b547162e592", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.0" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "deltaUPrime = np.diff(bins) \n", "M0 = np.sum(F*deltaUPrime)\n", "M0" ] }, { "cell_type": "markdown", "id": "geological-control", "metadata": {}, "source": [ "The moment of order $n$ is defined as\n", "\n", "$$ M_n = \\int_{-\\infty}^{+\\infty} u'^n f(u') \\text{d}u' \\tag{11}$$\n", "\n", "The moment of order 1 is the average of the samples, that should be 0\n", "\n", "$$ M_1 = \\overline{u'} = \\int_{-\\infty}^{+\\infty} u' f(u') \\text{d}u' = 0 \\tag{12}$$" ] }, { "cell_type": "code", "execution_count": 34, "id": "32f65226-6483-45ec-97ea-f61a7b1bdc1b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-0.00034572943202194895" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "UPrimePDF = bins[:-1] + deltaUPrime/2\n", "UPrimePDF\n", "M1 = np.sum(UPrimePDF*F*deltaUPrime)\n", "M1" ] }, { "cell_type": "markdown", "id": "familiar-funeral", "metadata": {}, "source": [ "The moment of order 2 is the variance of the samples, that should be the square of the standard deviation given by pandas before...\n", "\n", "$$ M_2 = \\overline{u'^2} = \\int_{-\\infty}^{+\\infty} u'^2 f(u') \\text{d}u' \\tag{13}$$" ] }, { "cell_type": "code", "execution_count": 35, "id": "intensive-scratch", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.2646119129824565" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M2 = np.sum(UPrimePDF**2*F*deltaUPrime)\n", "M2" ] }, { "cell_type": "markdown", "id": "faa003f5-ac5e-4055-af0d-56381dba4ec6", "metadata": {}, "source": [ "We can check it easily with the statistical data" ] }, { "cell_type": "code", "execution_count": 36, "id": "curious-interview", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.2646066292139868" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "statData[\"y = 0mm\"].loc[\"std\"]**2" ] }, { "cell_type": "markdown", "id": "revised-amsterdam", "metadata": {}, "source": [ "The moment of order 3 is \n", "\n", "$$ M_3 = \\overline{u'^3} = \\int_{-\\infty}^{+\\infty} u'^3 f(u') \\text{d}u' \\tag{14}$$\n", "\n", "The _skewness_ of the $u'$ distribution is defined as \n", "\n", "$$ S = \\frac{M_3}{M_2^\\frac{3}{2}} \\tag{15}$$" ] }, { "cell_type": "code", "execution_count": 37, "id": "olive-japan", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-1.9216881739274576" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M3 = np.sum(UPrimePDF**3*F*deltaUPrime)\n", "M3" ] }, { "cell_type": "code", "execution_count": 38, "id": "quality-occupation", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-1.351285182374243" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S = M3/M2**1.5\n", "S" ] }, { "cell_type": "markdown", "id": "nearby-generation", "metadata": {}, "source": [ "The moment of order 4 is \n", "\n", "$$ M_4= \\overline{u'^4} = \\int_{-\\infty}^{+\\infty} u'^4 f(u') \\text{d}u' \\tag{16}$$\n", "\n", "The _kurtosis_ of the $u'$ distribution is defined as \n", "\n", "$$ K = \\frac{M_4}{M_2^2} \\tag{17}$$\n", "\n", "For a normal distribution, it should be 3 (check it)" ] }, { "cell_type": "code", "execution_count": 39, "id": "prompt-vegetable", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "8.337551070336596" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M4 = np.sum(UPrimePDF**4*F*deltaUPrime)\n", "M4" ] }, { "cell_type": "code", "execution_count": 40, "id": "indirect-sharp", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5.21343507900745" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "K = M4/M2**2\n", "K" ] }, { "cell_type": "markdown", "id": "76020f00-1550-4968-9788-c787c7241b3d", "metadata": {}, "source": [ "## 7. Power spectrum\n", "\n", "Finally, from the time series signal, we can get the spectrum in frequency by performing a [Fast Fourier Transform](https://en.wikipedia.org/wiki/Fast_Fourier_transform) " ] }, { "cell_type": "code", "execution_count": 41, "id": "verbal-berlin", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "E = np.abs(np.fft.fft(uPrime))\n", "plt.plot(E);" ] }, { "cell_type": "markdown", "id": "f65b39b7-4fda-455d-b925-f560d81d437a", "metadata": {}, "source": [ "We compute the frequencies range, providing the periode of the data acquisition" ] }, { "cell_type": "code", "execution_count": 42, "id": "fundamental-shame", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "freq = np.fft.fftfreq(uPrime.size,0.001)\n", "plt.plot(freq,E);" ] }, { "cell_type": "markdown", "id": "f45e51be-f855-4722-a071-ac43ed1ace0d", "metadata": {}, "source": [ "and we keep only half the data, since it is symmetric" ] }, { "cell_type": "code", "execution_count": 43, "id": "occasional-hamilton", "metadata": {}, "outputs": [ { "data": { "image/png": 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YFoY9E1Ie+NSbaGqPAgC21xzu4ZYQBNFb8b64K2yZWFxzpEIKVLZMOKYexBSN9c4OVfvkJARBEHZyQNw5AvbIXePWQUzStqBiEJMYvWovPxDtpZG7oHfeegiC6A14Xtw1xWQd9sjdl6pDNaaeiSmWRc89m4jLoZLEBEG4kQPi7pysI+bw3CVbRhW5uwxiyla2TLYhW4YgiFR4Xtz1kr9OW8Y+QlVgt3CAROTu8Nx7aeROEASRihwQd2fJ37jNK5cjd0ftdyQ6VJ22TO+M3EU76dZDEIQb3hd3OFMhY3FuKSZmGcTkTxa5e8OWiZvTAvZwQwiC6LV4XtztRcIAvbyvqy2TLHK3re+ttWWooBlBEKnwvLhz7vTR9WwZ60xMArs/D8iDmLqntoyd1nAMVc0dnf58nIuZo5Lz83+7j2AlCCK38by46zMxOUeoutWWCdqLv0MexJT98gOqdMXHFmzD1U8t6fQxY2lG7n9btMt1WySmoXLWHLy8bE+n20EQRO/F8+LOOXfmuWuaa/kBZeQe18A5d3jY2fDcVRZK/eEIGto6XyUynoWbjihh8ODczV0+FkEQvQ/viztUtoxzJiaBaoQq53o07EyFzIK4KyL3qKZ1SaDNyL0LPariiYJR0jxB5CSeF3dVh2rUHrlL24KKyB3QbQp7+YFsjFBVVTCIxrlS9NPFzJbp9BESA7dI2wkiN/G8uHMO2IPxWNxWW0buUFV47oAh7t0wE5NKxGNxrUsZL125MQhEP4NiTBdBEDmA58VdXc/dPhNT4tW+r7B0wjHNWX4g1j2eezTOuybumnrQVSZETHEndSeIXMTz4u5a8lcexGS8+n3MEakWBPXJOyIxzeG5L9pW2+Xp6jSFiMc0LWX0vflQC+5+c6368xnYRW7FxcIk7gSR0+SAuDtL/joGMRnLPsYcHYj5eYa4x+OOSLglHMPs1Qe71D61LaNn5qiEW/Cd55fjhSV7sL+x3XnMDKJ+t31F5E7aThC5iefFXV3y1+6566965G7dV0Tu4ZjmyHMHgHbbPKVtkRgqZ83B35fsTq99SltGF9Zk0bvo3FVl7MTMDtXUIu92DvFEQpE7QeQmnhd3DkXJX802E5NhzKhsmfyg/hVEbP76Y9ecDACOSagPGJH03z7dmVb7lKmQQtyTRODimg6HY45t4iaUjuce1zg2HGh2nIsid4LIbTwv7m4jVFWDmDKJ3IeVFQAAWsNWcW/u0MW2OD+QVvtUAi4i72TiLtp5uMMp7sk8d7vHvuFAMy5+dCEe+WCLZT11qBJEbuN5cYfClgGgnInJz5gjUi0K6SLdHrV67uXFIeQHfWiLWMW1oVUfWVocSk/c5Tx3UU9GlDVIZsuIdrYoIvdkVSHt94t9DfqTxtr9TZb1YYrcCSKn8by464OYnOutc6gaHao+5ojyhbh3ROKWyL2sMIiivABaDXFvaI1gyY461B3OTNxlAZ/2q/kAEgXJko1SFe1URu5JIn63ssX2CJ0id4LIbXJC3BmcAiVbHkyK3O1iVixF7rJmFocCKAz5TVvm2meW4uqnlqDmcFjfng1bJknk7kviuZt57orPuRU/s98AEx2qrk0gCMLDeF7cOdQC1SgV5hJRvN/ntGUKjVTIOWsOor41bPlMUV4ArYa4rj/QDACoadH3sXfiuqHKwEmnQ5UlFXf9VZXDbi93IEfuW6pazPWmLaO4MfYEr6/Yh9/P25J6R4Ig0sL74s6hNI7lcr1is8/ntCFE5D5/UzXmrq9Cv4IgVtw9E4Bu2bRFrB2qQtzDaY5eVY9QTS3uwrppUdgyyUaoutky72+owvm//wTLdtYD6H2e+49eXY0/zN/a080giJzB0+IuIldV5C6Lsi+JLVNk884L8/wYWBwyl1ttHarNHXqp3HRHriptGdGhmkTcRftbjPMJOOeoN55KYoqqZKlq0u+qawUgp0L2EnUnCCKreFrchTaqrIV2SZST5bnnBaxfgbxZtmUEIu/dnhfv3karuGoaTytyF1k69sj91RX78MKSPa6fd7NlBOL6RORun0zci3RE40lH+xJEX8TT4p4scpdHlpqRu4850ibttoscycodqoKOqC6GnbVlInEtrQ7VVqNd9ieEj7fUmMu76tpQOWsOdtW2mutSTfItrk/cnLIx21RPEo1rGHfPe7h/zoaebgpB9Co8Le5CN1V57rKmigk6fApbRnjoAnlzUV7AkecubhrpirtdbCNxLaUtE4trpvjaqw8EFdf63vpD5rL9hhFxmXAkEtevIxsTkmQTt0Jnboj2v5BmOQiC6Ct0SdwZY7sYY2sZY6sYY8uNdQMYY/MYY1uN1/7ZaaoTVSaKCmG9qGyZmhbrRNWy+Bfk+R21ZYQts2J3A55euCPlue3aGYlpiGrJbZmDTYk22W2TgGImKTkX3v6d2EezmrZMVETuvUvcM32SEN+h159ACCLbZCNyn8E5n8Q5n2q8nwVgPud8LID5xvtuJdVAnGSRuz3V0DLfqo85xFHYMgDwizkbU7bNLuDtkcRI2LjGsWJ3g6M0wOIddQD0TB77gCV7BUxA73QVNx37/c7eNyCuT0T0vU0UMy2x3JW6+ASRy3SHLXMpgOeM5ecAfL0bzgEgEaWmSvgQkXtc45Z9v/vlMfjt5RMt+8riH/AxxDSOB97dZK6zFxJLt40C2eOPaxyXP/EZHvnAmgK4fFc9BhTlYdyQEod4qeaAfW7xboy75z20R+KO/e3tFdvFTStbkfunW2txx2trAAA7a1vNVM5MkW+e6ZBstC5B9GW6Ku4cwPuMsRWMsZuNdRWcc1EE/RCACtUHGWM3M8aWM8aW19TUqHZJfXLhuacSd0MQ7fOt/vSi4zFyYKG1XdKysED+/PF2c53dpkmFXWzl1Eq3DtWm9igGl4QQ8DNn5O4yByygZ9jYbyYdtsg9avP7syXu1z6zFP9cvhe1h8OY8buPcO/b6zt1HIrcCSI7dFXcz+ScTwZwEYBbGGNnyRu53jum/OvjnD/FOZ/KOZ86aNCgTp3cjNxTjLKUI/dUFo682V6HRhxD5s431mL5rnrX49kFvC1sjdwFcipfJKYh6Pch4PM5zpdqZKz9fvHv1Qcs7+215LMxCbhMc7uel//O2s5NckKRO0Fkhy6JO+d8v/FaDeANAKcAqGKMDQUA47W6q410Pb/xmrYtwzlU82OLEgSA1ZYJJomSBS8t3YOrnlzsut2efy17/LJwyzeBSFxDXsAHv88ZuScvGpY6kk1k4XDzeNnMERfX19AWTbFnAjlDJtPInfLbCUJNp8WdMVbEGCsRywDOB7AOwNsArjd2ux7AW11tpBvcCPJkQX7hxmkYP7QUN5052lwnfGq3yH3h7TNw3njdPbJG7ul9PclGeTpsGUncZWGS94vGOPL8PgR8zJEt45baCOhPMqkyiNqjcTS0RqznS3Mg05p9jaicNQeLt9c5tomnHFW5hFTIaaUUuRNEduhK5F4B4FPG2GoAywDM4Zy/B+ABAOcxxrYCmGm87xbsHaoXThiCM8eW453bpuPur4w39xOReyyuFveBxSGMG1KiHwuZRe76Z1K3USDnzcvCJC+H4xqCInK32SbhJOIX07ijnrudh+dtwcn3z7Nk0Xy4sRqPL9iW/IMAPjNEfcFm58OYsIvs5RLSQRb3cMZ9Gr0rlZMgegvp1a1VwDnfAWCiYn0dgHO70qi022C8+hjDrgcucd0vzxBpt9rvgJ7TDlg7GANpRu4a53h0/lb4fQznHj8Y44aUmtvsgXarnC0jCb9c2z0S0/TI3c+UI1zdiMdTR+4C2f743otfAAD++8tHK/sZBGKLsFH21LVhxIACMGbUyY8nZqrKBLkt6Q4OE1DkThBqPD5CNbNUyJjGXS2UQmO6PTkbRpVTDgCXnDTU1g49In5w7mbc9NxyyzZnh6rkucflyD0hatG4hlDABx9TiHsSTzqmqSf5VqES0UPNHYo9E4ivjnNg0bZanPXgArxtdNgGFLaMXBYhaVuisi2TOnKfveYAnl20E0D2O4QJIlfwtLgLHUtV2TDPrwu3prlH7qGgInJ3sWUmHFWKK6YMV24ryrM+DNk7/Nwi95jG0dgWweLtdUa2DDPz7GWSRbZxjTsKh7mhOs7uFGIsLCsOYI6RDVPdbNS39zttmdlrrJk67m3JLHK/9aWVuO/fei0ZSoUkCDUeF3eRCpkc4Z3HkqRChozoXvai3SyKPL/P1Y+vORzGwq2JvH27+Midkd/9+wpz+fbX1mDS/83DN/+yBG2RmJEt40yFjMQ0fKmyP37x9RMc546n0aEqH8fOrrq2pJ+RI/c1+xoBAAOL8wAkLCw5cl+5p9Hy+eueWapMkezIMHKXsfRb9LJSCgTRk3ha3M3CYakid0O4NY27C7axjzwcXzUaVOzrtq2+NYLrnllmvrfbMhsONis/J1d7bGyLIi/gMyJ3W7ZMTDO32Yl10nMX7G9MLu4CjXPsNybeFk86CVtGj9yP6pePPfWJ43HOsXBrLVbuaVC0pfPiLt/8Mh1gRhC5jKfFncO95K+MmQrJuas/Hwo4bRm3G0HQ7y7udjqThx3TOIJ+H/x+5iw8Ftc7W90GWKVrU6jsj1RpjPJNNFG+QH+1p0IePbgYe+rbzOsX7bKXWNbbkljXnnEqZGJ/EneCSOBpcTcn60gh7iGpQ9Utypc7XQVu1oubuJdIszp1RPU6L8lqtidDROf2VL9wVEMo4FeeP51USPk49ug/lbgnbBlu5sabkbvfJu6DihGOaeaE4uJ7VQlwozTgyV5iORXy16PqXN18qMW0kAiiL+FpcTc99wxsmVSeu4zbICbdlnEep7QgaC6Pu+c9fPvZzzs9gjLkV49QlUev2olrPO166OFYHPlBv2Vdqhx1MxUSzto0fpstc/SgIgDAvoY27G9sx7h73gOgV8W0s68hYd+oJgRPhhy5q8T9gkc+wdceW5TRMQkiF/C4uOuvqTtU5chdvY9K3FUTYwB63rwycs+3Zsp8vKXGYpMMKgmlaKl0bnOEKkcsrmHzoRYAKTx3TUvbltE4kB9MXEP/wmDaOeqcJ+wY8WpPhexXqHe0/vPzvTjjgQ/Nz6oi9/0N7SjJD6CiNOSY1jDpNdhsqGRjAAiir5ET4p5uhyrgHuXb51IFkmTLuHSo2iNhAJCDSdUNxA2RLRPTOH47dzMueOQT7KptRTgWRyhJ5J7Jg4LoZwD0UbqpbBnxFCE/TSQid/3axA1CjBt4Zfk+yzFUnvu+hnYM71+IolDAMa0hAFQ1dyg7WuUpC+W2EAThcXEXmSGpBpLKwu0m2LLQCVSzHgHCc3ceR3Vs2ZZR3UDcSHjuHJ8bVSf31LehNRx3vbnEXGyZSSPKlOeQI/cBRXk4HNYtlfrWCH797kZHuqSI0uXJx4WgivMKW0YuxiajEun9je0YVlaA4lDAYcu0dEQx7Vfzcc+b6/DJlhr86JXV5rZI3PqkQgOaCCJBToh7ypK/khBmYsu4jVB161BVleOVO1TzUmTYvPSdaZZz+H3WEapPf7oTHbE4zhtfoY7c4+oOXLcbmvykMbAoz4zcH3p/M578eAfeXWfNSRd55HL0LQRVRNAiC6fARdxVkXt1SxgVpSEU5QUstkzd4TBOvO99AMDqfY14b/0hvP5F4kkgErNG7tm2ZRZsqkZTe+a1cgiiN+BpcU+35G/QIu7pd6i6jVCVI2f5cKpDyxNwp7JlBhTlWc4hbi4i+t/f0IaygiBOP7rcxXNX2zLipmO/ucjiPsAQd865+b022sr2RhXpjEJQ7QOICvPUZYvsHaqcczS1R9G/MA9Ftsh9V11ixOzo8iIcaGy3fDYc0yzZRMkGMVXOmpPRaNaq5g7c8OznuO3llWl/hiB6E94W9zSzZeTINVWeu4xb4TB5hOpASZBVN451+5uSnkOmrCBxrFDAZw7pX71PP4YY3ASoLSPdc3cKmLiMcUNLLOtlW2ZgUR7iGkd7NG6mdNotEiGezVJWjT1yB/SnIzcLyt6hejgcQ1zj6FcQRHHIb5mpqrldXw76GZrbY+bAKUEkplmsmFTzwR7OoKiZuAltrzmc9mcIojfhcXHXX1MNYgJ08brz4nEp89xlkkXuYn852lbZHxsOJEakhoLJv25ZbEW2jExje9R8YlCdq741jD2KEgLiJjV11ADr+QLWyB3QBdVnHLu+NWLZXwh4s2RVRM3I3SqsbpaWPXIXTwf9CoOODlVxExnRvxBN7VHsb3SKuxyNf//FFahucS9+1qxI9axpCWP0T+eY/RoCcu8Jr+NpcTcHMaVMhgRW3HMebj7r6MzEPYnnLgRTFvfJo/o79m0Jx1BerKdApvLc5Tboo1Ct+8c1nojcFW275631yrlLhViPrSjGQ1cmqjTLtszRg4sBAFurW8wId9Mha6kEIeSyD23aMpqGUiMVVOPupRvao3FLp684VllB0NGhKrYN61+AvfVtDr8+HItb+hiaO2J4aO4W5XkBPQrfaSuO9sWeBnAOPCnNkwuoa+8QhJfwtLinW35Axm1fVSTsli0jD2IaWJTIXf9/5xyDB684ybF/cchvfi4ZsvjnBXxQPTiIfZJNlG1H7Jrn9+G4IQlrRn6SmDiiDIzpxb6EwC7aVof31x8y9xHRuZwPL5chGDOo2FyfrH1yoTARuZcV5qEwL4BITEN1Swd21baaTwgjBhSiRZH/bo/cU/Fff/scM373kWWduMHZZ4DKtMYNQfQ2PC3uoi8tlecu48vgTuAeuTMEFbZMwO/DlyoHOPa/YMIQADCn8nM9n9+H6WPLAeidln7FzSURuaf/XyduXKGgNT9ejtxL84M4dnAJPthYhab2qGkRicFTQGI0aFyRWx6LaxgxoNBcH0zSPtl3b2zXrZ+ywqA5COyUX87H2b/7CM0dMeQHfeaTjx27594ZxP+xXcwznTQkEzqiccuoXILoDrwt7mlO1iGTasCTjJu45/l9ZgQtizuQKIErc/ox5dj1wCWYNmZgynP+7sqJuOiEIThtzEDl+fOSeO5uiH3tpYrzbR283zlrDNbsa8KHm6px0vAyDCjKw0FpAg97h2VxKIBoXMPMhz9GaySOIaUJEU4Wucv1Y0zPvSCI/kVBy37N7VGU5gfRr8C6XhBOEbm7bZPHHgj7pSPmtHxkvtjToPTsO8OtL63Emb9ZkPXJvXfUHMabK/dn/LnVexvx0Pubs9qW3XWtqJw1R1nimTgyeFrcBZkIdiYWjmu2jJQKaRfzknynEBUZOd+ysLpNC1hRmo8nrp2CfoVBpYCL86Y7vysgiXvA6uPn2zp4zzym3FwuCQUwpDQfLy3dg4Vba/Drdzdia1WLZf+ywiCicY5t1YfN4wuS2zIJ4RS+er+CIPoXWr/LpvYo+hUETS/fTtiW527HzTc/LN1chIjbbRl5dqi2SAzf+NNnuPWlleCcW9rPObd0mqfDBxur9HMmmVUrE2558Qt8uKkKX3tsEX7wz1UZ3zQufXwR/vjhtqxOfLLe+E7eXpWYsIXz9GsfEV3H0+KeGMSUPplYOG4CFfT7cPSgIkwaUYbJI52dqHZEzncyq0J5flXkHsgscp8+tty8+dlr0tj7AOTaOCX5ARQbKZHXPbMMT368w0zJBPRUzYrSfNc5Z5Ndq9wx2hqOIeBjyA/6HeLe0BZBaUEQUxVWFyBGqLrbJ27i3iTl7wtRt2fxyLbMwSb96WXjwWY89P4WjLvnPbNf4vnFu3HxowuxZEcdMkVVRE1FOBZ3Fd5oXMOctQfx7WeXm23q7MCrTCtyJiNRZC7R7q//6TM88sHWrJ2DSI6nxd1MhczgKjKJ3GUB/fBHXwagW0ABH8PA4hDevOUMVJYXpTyOGIofzKD8gP38gkw89+ljy/GXb01NeO4Bv+WGZR9RW5jnN/ctzg9gR5Jp90YMKESe32fxvIN+hvsvnYCfXHBc0r4NWdTao3EUGN6/3eLaVn0Yg4pDGF1ehJ9ccBxuv/A4y3b7CFWZWFxDfVtEua2xLYpDTR1Yu6/JjNztNoyIzvfWt5tjFUrzA5hrdDC/tHQ3AN3S0PfL3ENPt/78cXe/h5ue+1y5TVUPqK41rNgzNarRw8nYWtXiWs/HHkNpGsf6/U3Y6DJZDZF9PC3u6ZYfkElm4dz71fH44zdPNt/L6XyiomPQ77NE/6nSGwGg0MiWcfPw3VAJeCbZMoNKQsgP+iVxt3ao+m3HYIyZFlJZQR7+55xjXI89ckAhggGfZch/XAOuO60St8ywfm54/wLL+zZJ1DqiGvLFOQutllbt4QhOGa1H7bfMOAbfP/sYy9NFsoj2x6+udmTGCJrao/jKHxfiq499akbuDltGitxve3kVAP0JbNRA/Wa+s1YXc3FzySR7SfDxlhq8sTJRTmHZznrLU4XMgs01yvUio8jvY2bgUntYfVO747U1uPgPC13bk4m4H2hsx3m//wS/nLPRZQ/nGI2YxlF7uHM3HiJzPC3u6ZYfkEkm7jecMRpfnXiU+d4ihFKnpIzK+z77uEGW92LS7HRnb1KdX5Asz92OuOn5LbaMVERNVQvHEKvy4jxcf3olXvvv05THHtG/AEEfs0RurS6P9f973rGW9x2ROJbsqMOhJr3ao/D+i0NOb/30Y6yd0HIRtPZI3DVyf3OV++Tcje0RUwBFeQhntoxT6NbubzL98nojOhZ59m61/+3IJRLuemMdfvjP1Vi9txFtkRiuenIxvm2L0N086rZIDEt21JmdvAEfM38bdQpxj8U1/HP5XuU0j+JnkEm5ZXEO++AvqeVG+/V3YnBZXav6xtMV9ta3ZTwPQF/A2+IuqkJmlArZuXPJvrWMysP/87VTsPD2GeZ7YTtkkuGiH1t/nXl8BS6YoKdRdiVbxhG5K44hIvFBJfkA1B3Ek0eW4bzxQxD0+yzD893+wOxlF9oicVz91BKc+uv5aI8kbBnVdzm8f6Hl/W+vOMn8Lpo7YtA0bqnZk6yDVSB70luMTuKYxi2CnioVsqFVP0ZcTDPIEnWAvvv35ZZJ0gF9QvGnF+5wjPoFgE+31WK3MbJ4xe7EHLP3z96AB97dpDz/3W+uw9VPLTE7c4NSBlddaxhr9jVarkcWdbu3Ln7bmUxTKNJi3X6H4vsT/xvVzfrNsLbFGblrGsczn+5EWySG6pYOVM6ag7dWpZ/1M/23C3DNX5akvX9fwdPinu40ezKZ3AhkxI84nSyV/KDfkvOdSW69jPCz8wIsEf0HRDvS/6/zSdkycvtVf5gi3bHcyAKyT0AybfQA/Ov7Z+DMseXw+ax2hlvtFnvBNNmWOdTcYYo7oNs9MkW26pJD+xXgyeumol9BEE1tEXO+WUE6GSgfbqw2l9/fUGUuiyj+R6+sdhVVgfC1xc0kEtfP2xKOYe76Klz3zDKs2F2PFw1v/vInPsMv5mxEVbNT3BpaI9gtFUnjnKPucBjPfLoTT36yQ3n+TQf1m5LIVApKE8h8sbsBX3tsEX79TuIa5BuaPbL3dSJyF/0mbgkKpribkbt+3a2ROFbvtd543t9wCPfP3oAH5242+y6e+XRnWu0Qx1kjdfZni23Vh3Hjs597dkCbp8U93ck6ZDoj7gVBv8XaOFKI6Cjo95m+fZ4/vaeAYWUF+MHMsQASFo59Yu1kxyg3+hhKbTnmspAearLWcXETB3tNnSapo3PDgWbLYKqPf3I2XropUfrYTTz6FQTR1B5FXOOW6xApjMluwvM3VSvXV7eEwTm3lBV2Q0TgIlsn4d0nhODyJxbjrjfWWYR13QGnCDW2R7FLqglU1RzGRy4e+1VPLsbjC7aZJZXnGTZRwO8zPfNNxsAzee5Y2U+3WyPiO06VvXP3m2txn1HeQjylyT+hB+duwj+W7cHP/70ei7bVGmv1mcQOSnWBLn18Ee56Y535Xjwx1LdGzAnh0834sVcuzSZ3v7kW8zdVW56mvIQ6gdgjdCYVMtMg+oUbp6GyvNCMfjP1zZOx7K5zAegjMlWIVL6g3+eI3N0894eunIhoXMPVp4w01/ncPPdk4m6MCrVHznLH4W5bkbIrpw5XHss+Q5Xc4ReJa5ba74wxFCm8dztlhUE0tkdRnB+wfBcikgsF/IjGdQF6+eZT8c/P9+KNFAN8qpvDaYtFQ1sUf5y/1Yzc522owrvrDuG+r4537Dvx5++by6rJuhvbIpbvsrE9gh21zmqU1c0dWLazHst21uMMoy9CfM7HEiIpnkAONXWgsS2C2WsOWgZg1dk6NcW315pC3F9YsgcAcN/XJpjiLttRjy/Y7vgM58D5j3yCHTXWzKvPTPFP9A1pHOaEMW7/D9N/+yGOqyjF09dPBeAsbtcZonENh5o6LE/bou16+zrPT15djWljBuKKKeq/je7E0+JufvkZROOZ7AsAZ45NDOzx+1ha2THpMtjwtd0QFknQz8xc+ZBZR159HZXlhZhiq/4op0JaInfGMPP4CowamPhRjxxQiD31bebAIft55JuDHAE+/a2pmOlSXsFuy9hzwgts4u820YeMiNyH9su3XFNHNI5dta36E5ahYXkBn2PAFgCMG1JiRrkAUNPSgaokVSXtPDRvC04/WhfZD42nAZXtIrN6rzNyb2iLQpaQpTvqlUL5ydaEIC7aZv0O28LOyPxAUwcm/d88x3HskbvpuUte/Gfba7Grtg3XTBsJOw/P24JBhm0nPruzTp02ywGHsAOwzDsgcuE1zs3UTrfIfW99O/bWJ54Clrt26DqpPRxGazhmZjwJ/veV1fj36gPYdP+FlkDEbGKaknHO7z5CSX4Ab916JgA9OeHVFfvw6op9PSLuHrdlMi8c1hX8UkZCOiy8fQbe/+FZnT6feOQPBfwoSrP4mOqG4dZf4PcxPH39VNzzlUS0+dr3TsNr/32a681DPsYvLzvBXBa2kQp7h6osqIBC3BVz0drRPfcoYnFuidw/39WAcx76yBLRlYQCyvlt5c5aH9NtmVTiDADHDy01l+0duIea2+27W1BlqzS0RVDXGkZ/IxVUVdkTSOTUq1AVVnPjpaV7LKNYTc9dityv+ctS3PnGWlNkZbvp0flbzeJx4mfi1jY5VfWofonfpsgy2lvfhp+9qV/vvPVVlt+GfaStvcN+W/Vh3PNW4rtKNvq1vjWCqb/4AJc8+ilicQ0Pz9uCaqO0xr9X65lVjhuKcbhU8wQIdtS2Wgb6HWxK/lvobjwt7lonIveu4GcsI1tmxIBCHFtRknpHF66YMgJXf2kEfjBzbGKUa4rzi3x8mcqBRRg7uNjxPalsmcEl+a4jQgHrDEv/OW0UJo8sA5B8UFWqGajy8zofuUfjmiNfX+5ov/uS4zG2ogQXnTDUcYwRAwqk5UJsrzmMqqbUkfukEWX45ikjUV6c58iqOWj7/PSx5ZabgYrGtijqDkcsVTUBZ9Cydr8z6v/dlRNx9KBEJJoq0Jlx3CCs2tuIMXe+g8cXbAOQiFCFLy+L5ALjiaTGluUi+ls0zhHXOB4zjmVHvikMLk2IuzjHd55fbt6YInENT3yUeGKx1++3F1uzWzLVLWF8tr0WkZiGmpaw5cYiOp4Ph2P4ZGsNHp2/FQ+8u8myj2wFLdtZj2XGU4Hoi4hrHHPWHMTk++el1ckqP2GoaO7Qrb1FkkWVTTwt7p0p+dsV3GyZFXfPxKqfnZf18xXk+fHA5SehrDAv7chdFaFeM20k5v3vlx3rM03NBIDBpdabhxihm+z+mnKSkkDnIvfG9igONnW42lt3XDgON00fAwA4ZfQA7HrgEtxwRqXlGIITjuqHdfubTXG+fPJwM5K2E4vrtetrD0ccEau9k/mv//UlTDXq/J8wzCnyFaUhNLZFUHs4jNHSaOeiPD+evG6qZV+7uI8cUIgrpgzHJScmblxi0Jcb3zqt0lx+cO5mxDVu3qDaDJGVn17ueXMd3ll7EFXN1usSUWlbJI4tVS3YUdNquckIOqSbn/y3IzR1i61ekczW6has29+E+2dvQDSu4cJHrAOwWmyF3O59az2u+ctS3P3mWnzplx/g1+8kBljJN4LPd+kdpHHOLde1t77NvK6rnlxsrm+PxvDBhiocfec7uP211ahvjZgjlQE94lc9Ncijlu1TQK7b34ST7nsfD83bgqWdKF2RDp723DuTCtkVfExdQmCgS0nadLnnK+MxaUS/pPuIiDmb2TqdEfcK25PB/116AiaP7G8KmIpU0wsW5FmvSYj7zOPdSyRXlOYjrnEs3VmPb5w8TJnRoBoUdefFx6O5PYbXv9hneeyfMKwUc9YexOIdtRg1sBAPXaVPavLkx9vx63c34YYzKjHz+Ar859NLccWU4VjukkEhxP6FG6dhwlGlCPp9ZjrpuCGlWLffasscPagYVc1htEXiqBxYCMb0vqTJo/o70kLjmm5BCStIDJYTTz4Di/IMq8ndh7aXeNhb32ZGr2IQ2tbqhOC2hGP4/otfOI7zgZFO2h6Jm9/9RScMdUTwHZLVI0+sIiLfZMMSFm6txaq9jVi5p9HSLyTOa+90fc8Q3MWGWD796U5E4hr+79IT0CBlaH1sZCK1huMW0b/p+eUAYBmlDgD1rVG8v17PShLjQG57eRXmbajC5ZOH44ZnP8dz3z7F3L8tEkNhXgB7JHE/5q538ZvLT8R/fEnvw1i8PSHoR5VZR3BnC29H7mnOoZotstGh+vg1k/H3G0+xrLvxzNGOTlA7icqS1vOPGVSE70wf3am2qEaoqnjrljPMZfnRGtAF9NpTRyX9P3CzZcRcrfZI3edjWHj7DDx2zcmqjwGwRqijBhbhkpOGIuhnqJREwC5kgP79iX2iGkd5cQjjhpRg+jG6UC7ZUY+ThpeZ+wshzQv4cIZUutme/y8QnmtleSH6G+cX6aQ+ptenKZRsp4ukqHtQScj8TkoLghha5nwiOd8YwHXvV8fj7kv0vhLxmxw3tER5Q5OxfydnSyUaalrC+MXsDfjUsAkqSlMHLW2ROD7ZUoPy4hAmSqOHBXJ9n+99+WjL5+wTnguGlRVg3JAS/G3RLqzc0whA9/kB4GTDBmxoi5ge+aqfnWeZK0G2Q55frI8zkEVc9Hvsa2hTZtv8zz+sk6LfP3sD3l2n3zhk/332moN45AN95q8FUnpt3eEIFm6twbOf7bIc547X15rL8hPDsP7dI+6ejtyzkaqUCXqHatfOdslJTu83HUR6oCyUy+48F0WhAIpCAfxl4U7LY306pBu5TxxRhhOG6VHnYIWnnwq5zR//5Gx8+cGPAOg3ptX7mqDqB7Onpdk5TurLGDWwELcZOf0AUDlrDoCEENgRM2zFNY7PjXRUxhguOXEo5qw9iBMl++TaaaOwbn8TbjbsHYEQ98ElIUTimiOKlG9YYt+YxrHkznPBOfCLORvxj2V7cOroASjND6C5I4aBRSH0KwyiuSOG0vwgShWjg78zfQx+OPNYjJWuX6SWXjhhCA41J+8z6K+44QmW7KjHBxurzZtFaX7QYtH8YOZYR1XHQ80dOLShA7fMOFr52xBe/a8uOxEzx1dYplKcvUZdIqI4FMALN03Dmb/50Bw/IK7xmlNGYuWeRjS0RdDYHgVj+ijqP187BQeb2vH84t14SjHwSyXiu+vautzpKYrryWWf61ojuO6ZZQD0TuQDklX3p4+24dXl+yzTPQ6jyN1JwnM/MvLuy7BDNZsM71+AwSUhHC11ug0uzTdFf/3PL8C7t03P6JiZ2DIiRS2ZOLgR8PvMiFFOQ/uuEcl1ZgSvz8fw1HVTcNLwfq4+89B+6j8akfETjWtgjJlPHY9cPQl/uHoSrju10ty3X2EQT1w7xWG9lYR04S0KBZQ52XKnsOhT0DSOwjz9Zvzrb5yIlfech7EVJfjgR1/GXRcfj+nHlptlj90mKBldXmQRdgC44YxK3DrjGPzHl0aag9zcsI9bMK+zIGiKbiSuYUBRHs45frC5/bpTR+FkW3nr752diMS/MXk4Jhzl3nFcbNzgFt1xDhb8+Gz4fQyvr1CPOyjJD6C8OIQfn2+tAjq0X7550//eC1+guT2KklAAfh+D38cwvH8hRiii4KufWoy/LrKOeJ06qj/ao3HHzWqGrS5UKsTfxRd7EjbdIemGMWGY1W797XubHfP4ki2jQJTyPlLiXlbonFDiSDGwOIRld83ECcPU3nyRS7pfMjIRVfFI3dko4/0fnoX3fmC9+VwwYQhe+e5p+PYZnbOVzp8wBG/feqbjj+P3/zERD1810eVTuhBNGdXf7GwVBP0+XDppWFrZOiIad+v8lTuJxcCvqM1gFjfKwSX5+M5ZYxAK+M0KmqUF+vHt/Q5lit9fRWk+fnzBccgL+EzffEx5kVlCQka2z+Q03UsnHWXZb0hpPn58/nF47wfTceuMY/Dj84/DxOHW3558Axo5oBABvw8zj69QfifCbupXGMTo8iJMGz0Am22dqWONSdqPMV7t+ejHDC7GCcP6oSjPjz31bVi5t9HxfQxXPPEt2VEPzq2ZZF+deBTOGTfY7EAXN71JI9z7jtwYVlZgSYn9k5Tx41YjP8/vwzcmDwOgToLIBt4W905Ms9cV/nbDKfihrcKhFxH2TSYliK8+ZSR2PXBJp3+IuretR3bCm/X7GE4ZPSAtMc2Ey04ejm9Mdh80MqAoD69/7/QuPQ6Lv+UiKb9/9v+caS7LN07xhBRPI19a5N6LfZ+4djJW3D0T/3POMbg8yTUJRAbJDWeOxvK7k2dwHVtRgqe/NRWPXzPZ8ZQztF8+gn4fxg0pxY8vOA79CoMoK8zD1l9eZO4jT1Qjnmifum4K1v/8AnP9GCODptD2f3zf1yYYg/MStfzFE5h4Ahjaz9rnMHaw3qfwvpH5tXpvo+MJ5ySX4Aewjk8YVBLCz6TxHSJRYlBJCL+94iTL2A+BGLVtn9P3tnMTluCsi8ZZ6tz89KLjLZVMBRwcD105Edt/dbFre7uKtz134zVTcX/wipNMocmE7vLGjjSjy4uws7YVreHUubrdwYs3TVNWB/QSxw8tgd/HcNu5x+LaZ5YCgOtT1bghuo0yY1zqR36RTiiKqwX9PgwsDuFHNovCjRnHDcY/lu3FNJtVddu5Y01L46WbpplZV2JU8avL91r2n+yS/STbkhMVGV7ipvb3G09B0O/D26sPYEdNq6Pe/bEVJbj3qxOws7YVt80cCz9jqD0cRnNHDJcboznHDSnBNdNGYmBRHv744TYzoh9WVoDh/Quwr6Hd8XTilrl231fH44qpI3DCvXMB6CIuT7QzddQAfLCxCnkBH66YMhyt4Rjun73Bcowrpw7HEx9tx+SRZThn3GDM+pfeQXrFlOFYsrMOYweX4LtnjcFv3tsEzoGHr5qIE4b1w2v/fRrq2yKOMiOMMXRiGoC06TZxZ4xdCOAPAPwAnuacP5Dtc/BOTNYBAFdOHZHtpniKaaMH4MNN1d0+n6UoZWCnOBRImdXR2ykrzDOjrp9/bYJjwI3MMYNLsPpn55tWSzIuO3k49jd24MYuWFVbfnGRI2VWfuI8XZorV3BsRQkCPoYLThiCOWsOmpaBih/OPBaTR5UhFPDjD1dPcqRsAsD0sfqNbNKIMkwbPUA5HeW1p46yvC8KBSxpiAG/D7+67ERsqWrBnz/ejinSDWfUwELsa2jHiVJmk+BXl52I+95eb5lI5rLJw1EcCuC/Tq/EGyv3m0+vi2adg/ZIzChtzc30UvuThmjvEx9txyUnDbW0xedjePiqSYm2DSjErro2M8IP+H0YJN10QgEfHrzS3TbMGmLS2mz+gy7o2wGMAZAHYDWA8W77T5kyhXeGd9Yc4KPumM03Hmzq1Of7KvG4xueuO8g1TevW87SGo7yhNdyt5+ht/PiVVfz8hz/u6WaYLN5ey99atT+tfdvCMR6JxfmhpvZublXmRGJxy/ur/vwZH3XHbP7u2gPK/TVN49FYnI+6YzYfdcdsy2893d99c3vE/Pz6/brGxOP6Z9sjMT7qjtn8d3M3OT53/7/X81F3zOZr9jZa1otjZRMAy7mLrnZX+HQKgG2c8x0AwBh7GcClADYk/VSGmIOYjlgyZG7g8zGcP2FIt5+nMC+AHup/7jGOSESWAaeOGZh6JwPR91FRmrygXU9gz1K7+5LxuH/2Bpw5Vm11McYQ8OsZVVuqWiwdyemOiynJD+IPV08CYwzjjX4AYTvlB/3YdP+FyjEcsy4ahxnjBuNEWwf0H795cqdSiTsL493waM4YuwLAhZzzm4z31wGYxjm/VdrnZgA3A8DIkSOn7N69O+PzrNjdgL9+uhN3XXJ8t6UTEQRB9FYYYys451NV23rM+OScPwXgKQCYOnVqp+4wU0b1t3hfBEEQhE53pULuByD3Wg431hEEQRBHgO4S988BjGWMjWaM5QG4GsDb3XQugiAIwka32DKc8xhj7FYAc6FnzvyVc66egYAgCILIOt3muXPO3wHwTncdnyAIgnDH0+UHCIIgCDUk7gRBEDkIiTtBEEQOQuJOEASRg3TLCNWMG8FYDYDMh6jqlAPonunDey90zX0Duua+QVeueRTnXFmDoVeIe1dgjC13G36bq9A19w3omvsG3XXNZMsQBEHkICTuBEEQOUguiPtTPd2AHoCuuW9A19w36JZr9rznThAEQTjJhcidIAiCsEHiThAEkYN4WtwZYxcyxjYzxrYxxmb1dHuyBWPsr4yxasbYOmndAMbYPMbYVuO1v7GeMcYeNb6DNYyxyT3X8s7DGBvBGFvAGNvAGFvPGLvNWJ+z180Yy2eMLWOMrTau+efG+tGMsaXGtf3TKJsNxljIeL/N2F7ZoxfQSRhjfsbYSsbYbON9Tl8vADDGdjHG1jLGVjHGlhvruvW37VlxZ4z5ATwO4CIA4wF8kzE2vmdblTWeBXChbd0sAPM552MBzDfeA/r1jzX+3QzgiSPUxmwTA/Ajzvl4AKcCuMX4/8zl6w4DOIdzPhHAJAAXMsZOBfAbAL/nnB8DoAHAjcb+NwJoMNb/3tjPi9wGYKP0PtevVzCDcz5Jymnv3t+228zZvf0fgNMAzJXe/xTAT3u6XVm8vkoA66T3mwEMNZaHAthsLD8J4Juq/bz8D8BbAM7rK9cNoBDAFwCmQR+tGDDWm79z6PMjnGYsB4z9WE+3PcPrHG4I2TkAZgNguXy90nXvAlBuW9etv23PRu4AhgHYK73fZ6zLVSo45weN5UMAKozlnPsejMfvkwEsRY5ft2FRrAJQDWAegO0AGjnnMWMX+brMaza2NwEYeEQb3HUeAXA7AM14PxC5fb0CDuB9xtgKxtjNxrpu/W332ATZROfhnHPGWE7msDLGigG8DuAHnPNmxpi5LRevm3MeBzCJMVYG4A0A43q2Rd0HY+wrAKo55ysYY2f3cHOONGdyzvczxgYDmMcY2yRv7I7ftpcj9742CXcVY2woABiv1cb6nPkeGGNB6ML+Iuf8X8bqnL9uAOCcNwJYAN2WKGOMicBLvi7zmo3t/QDUHdmWdokzAHyNMbYLwMvQrZk/IHev14Rzvt94rYZ+Ez8F3fzb9rK497VJuN8GcL2xfD10T1qs/5bRw34qgCbpUc8zMD1EfwbARs75w9KmnL1uxtggI2IHY6wAeh/DRugif4Wxm/2axXdxBYAPuWHKegHO+U8558M555XQ/14/5Jz/J3L0egWMsSLGWIlYBnA+gHXo7t92T3c0dLGT4mIAW6D7lHf1dHuyeF3/AHAQQBS633YjdK9xPoCtAD4AMMDYl0HPGtoOYC2AqT3d/k5e85nQfck1AFYZ/y7O5esGcBKAlcY1rwPwM2P9GADLAGwD8CqAkLE+33i/zdg+pqevoQvXfjaA2X3heo3rW238Wy+0qrt/21R+gCAIIgfxsi1DEARBuEDiThAEkYOQuBMEQeQgJO4EQRA5CIk7QRBEDkLiThAEkYOQuBMEQeQg/x92ww2vhHP8ggAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "E = E[:len(E)//2]\n", "freq = freq[:len(freq)//2]\n", "plt.plot(freq,E);" ] }, { "cell_type": "markdown", "id": "7c3fe1eb-5e52-46ac-9ed1-1f502923f42c", "metadata": {}, "source": [ "and, finally, we compute the energy, which is the square of the velocity" ] }, { "cell_type": "code", "execution_count": 44, "id": "offensive-consent", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "P = E**2\n", "plt.plot(freq,E)" ] }, { "cell_type": "markdown", "id": "3c1fca37-fefa-4302-987a-01f55310fced", "metadata": {}, "source": [ "Let's plot it in a log-log graph with the [-5/3 Kolmogorov's law](https://physics.stackexchange.com/questions/13161/physical-explanation-for-kolmogorov-5-3-spectrum-in-fluid-mechanics) as a reference line for the energy decay in frequency " ] }, { "cell_type": "code", "execution_count": 45, "id": "ranking-motivation", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1)\n", "ax.set_ylim(1,1e5)\n", "ax.loglog(freq,P)\n", "f_plot = np.logspace(1,2.7,100)\n", "f_ref = 10 #Just a Frequancy and Energy of reference for the -5/3 law\n", "P_ref = 1e5\n", "P_plot = P_ref/f_ref**(-5/3)*f_plot**(-5/3)\n", "ax.loglog(f_plot,P_plot,'--')\n", "ax.text(30,20000,'-5/3');" ] }, { "cell_type": "markdown", "id": "7f074fe0-178a-4e6d-b05f-76efc805fa49", "metadata": {}, "source": [ "This spectrum can also be computed via the velocity autocorrelation" ] }, { "cell_type": "code", "execution_count": 46, "id": "authorized-electron", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rho = sm.tsa.acf(uPrime,nlags=999,fft=False)\n", "smg.tsa.plot_acf(uPrime,lags=999,fft=False)" ] }, { "cell_type": "code", "execution_count": 47, "id": "valid-pantyhose", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Pr = np.abs(np.fft.fft(rho))\n", "plt.plot(Pr);" ] }, { "cell_type": "code", "execution_count": 48, "id": "acquired-attribute", "metadata": {}, "outputs": [], "source": [ "freq = np.fft.fftfreq(rho.size,0.001)\n", "Pr = Pr[:int(len(Pr)/2)]**2\n", "freq = freq[:int(len(freq)/2)]" ] }, { "cell_type": "code", "execution_count": 56, "id": "blessed-series", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1)\n", "ax.set_ylim(0.1,1000)\n", "ax.loglog(freq,Pr)\n", "f_plot = np.logspace(1,2.7,100)\n", "f_ref = 30\n", "P_ref = 100\n", "P_plot = P_ref/f_ref**(-5/3)*f_plot**(-5/3)\n", "ax.loglog(f_plot,P_plot,'--')\n", "ax.text(40,100,'-5/3');" ] }, { "cell_type": "code", "execution_count": 50, "id": "76726e36-edb7-4b87-aedc-c05b57ff53a4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Python implementation: CPython\n", "Python version : 3.8.13\n", "IPython version : 8.0.1\n", "\n", "Compiler : GCC 10.3.0\n", "OS : Linux\n", "Release : 5.4.0-144-generic\n", "Machine : x86_64\n", "Processor : x86_64\n", "CPU cores : 4\n", "Architecture: 64bit\n", "\n", "matplotlib : 3.5.1\n", "statsmodels: 0.13.2\n", "pandas : 1.4.2\n", "numpy : 1.22.2\n", "scipy : 1.8.1\n", "\n" ] } ], "source": [ "try:\n", " %load_ext watermark\n", "except:\n", " !pip install watermark\n", "%watermark -v -m -iv" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.13" } }, "nbformat": 4, "nbformat_minor": 5 }