{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Notebook to Explore Boundary conditions for Standing and Travelling Waves ##" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What if you have a standing wave but put in the wrong boundary conditions. Or if you have a travelling wave and do the same thing?\n", "\n", "Lets start with a right travelling and a left travelling wave:\n", "\n", "$$\\eta = A \\cos(k x - \\omega t) + B \\cos(-kx -\\omega t + \\phi)$$\n", "\n", "where $x = 0$ is at bay mouth." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "x = np.arange(0.,200.,5.)*1000. # m\n", "A = 1 # m\n", "B = 0.6\n", "phi = -np.pi*0.55\n", "omega = 2*np.pi/(12.4*3600.) # /s\n", "h = 150. # m\n", "g = 10. # m/s2\n", "c = np.sqrt(g*h) # m/s\n", "k = omega/c # /m\n", "t = np.arange(-np.pi,np.pi)/omega # s" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x, t = np.meshgrid(x,t)\n", "eta = A * np.cos(k*x - omega*t) + B * np.cos(-k*x -omega*t +phi)\n", "plt.plot(x,eta);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now $$\\frac{\\partial u}{\\partial t} = -g \\frac{\\partial \\eta}{\\partial x}$$\n", "$$\\frac{\\partial u}{\\partial t} = -g \\frac{\\partial}{\\partial x}\\left[A \\cos(k x - \\omega t) + B \\cos(-kx -\\omega t + \\phi)\\right]$$\n", "\n", "$$\\frac{\\partial u}{\\partial t} = -g \\left[ kA \\sin(k x - \\omega t) - kB \\sin(-kx -\\omega t + \\phi) \\right]$$\n", "\n", "$$ u = \\frac {g}{c} \\left[ A \\cos(k x - \\omega t) - B \\cos(-k x - \\omega t + \\phi) \\right]$$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "u = g / c * (A * np.cos(k*x - omega*t) - B * np.cos(-k*x -omega*t + phi))\n", "plt.plot (x,u);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So for my current wave, $u$ increases into the \"amphidrome\" and $\\eta$ decreases. At $x=0$, \n", "$$\\eta = A \\cos(- \\omega t) + B \\cos(-\\omega t + \\phi)$$\n", "and \n", "$$u = \\frac g c \\left[ A \\cos(-\\omega t) - B \\cos(-\\omega t + \\phi) \\right]$$\n", "Apply sum and difference formulas:\n", "$$\\eta = (A-B) \\cos(\\omega t) + 2 B \\cos(-\\omega t + \\phi/2) \\cos(\\phi/2)$$\n", "and $$u = \\frac g c \\left[ (A-B) \\cos(\\omega t) + 2 B \\sin(-\\omega t + \\phi/2) \\sin(\\phi/2)\\right]$$\n", "The first part, the part proportional to $(A-B)$ is the travelling component (goes in, doesn't come out). This part has no phase difference between $u$ and $\\eta$.\n", "The second part, that part proportional to $2B$ is the standing component. Looking at it:\n", "$$2B \\cos(\\omega t - \\phi/2) \\cos(\\phi/2)$$\n", "and\n", "$$-2B \\sin(\\omega t - \\phi/2) \\sin(\\phi/2)$$" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ZY87ecS6j477+Y+jPQ9l/bj+zGs6yHcXnrVkDLVpAeDik1j0z4jR/93ymbJ1C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\n5eXLJl9SJkcZ23H80u7dTvO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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "wt = np.arange(-np.pi,np.pi,0.3)\n", "first = np.cos(phi/2)*np.cos(wt-phi)\n", "second = np.sin(phi/2)*np.sin(wt-phi)\n", "plt.plot(wt,first)\n", "plt.plot(wt,second);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So these components are exactly 90 degress out of phase. The $u$ amplitude is augmented by $\\tan(\\phi/2)$" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.258198889747\n" ] } ], "source": [ "print g/c" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The ratio of $g/c$ for 150 m depth water is 0.26/s. Raw ratio of M2 u/M2 amp and for K1" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.329203109815 0.457831325301\n" ] } ], "source": [ "print (0.271/0.8232), (0.190/0.415)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and the phase differences are M2 -54 degrees and K1 60 degrees" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So, as a guess for K1, say we have 1/3 travelling and 2/3 standing. That means B = 1/3 and A = 2/3. That is based on the lag. \n" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(30, 629, 23) (30, 629, 23) (30,)\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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PZkEDcFy0njly3aUntH5BYx5vdsnlfbzobJLxuWW2a4yP5rv8Fv/Jf3JG77s7qs+Jpxrt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\nwqzD2MOmuesZMqP+Rl4zMzMzs9Jc0FjNNc+sr4Jm5/odbFu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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "swt = np.arange(-np.pi,np.pi,0.01)\n", "AK = 2/3.\n", "sBK = 1/3.+np.arange(-0.15,0.15,0.01)\n", "sphi = np.arange(0,2.3,0.1)*np.pi\n", "wt, BK, phi = np.meshgrid(swt, sBK, sphi)\n", "eta = (AK-BK)*np.cos(wt) + 2*BK * np.cos(wt-phi/2.) * np.cos(phi/2.)\n", "u = (AK-BK)*np.cos(wt) - 2*BK * np.sin(wt-phi/2.) * np.sin(phi/2.)\n", "#plt.plot(wt,eta)\n", "#plt.plot(wt,u)\n", "phase = np.zeros((u.shape[0],u.shape[2]))\n", "amp = np.zeros_like(phase)\n", "print u.shape, eta.shape, sBK.shape\n", "for i, Bs in enumerate(sBK):\n", " for j, Ps in enumerate(sphi):\n", " phase[i,j] = ((wt[i,np.argmax(u[i,:,j]),j])-(wt[i,np.argmax(eta[i,:,j]),j]))*180./np.pi\n", " amp[i,j] = ((u[i,np.argmax(u[i,:,j]),j])/(eta[i,np.argmax(eta[i,:,j]),j]))*g/c\n", "plt.figure(figsize=(14,7))\n", "plt.subplot(1,2,1)\n", "plt.contourf(sphi,sBK,phase)\n", "plt.xlabel(\"Intrinsic Phase Shift Between In and Out Wave\")\n", "plt.ylabel(\"Strength of Out Wave (in wave = 0.67)\")\n", "plt.title(\"Observed Phase Shift Between u and $\\eta$\")\n", "plt.colorbar()\n", "levels = np.arange(0.,2*0.458,0.458)\n", "plt.contour(sphi, sBK, amp, levels)\n", "plt.plot(2.18,0.42,'*w')\n", "plt.subplot(1,2,2)\n", "plt.contourf(sphi,sBK,amp)\n", "plt.xlabel(\"Intrinsic Phase Shift Between In and Out Wave\")\n", "plt.ylabel(\"Strength of Out Wave (in wave = 0.67)\")\n", "plt.title(\"Observed Amplitude Ratio Between u and $\\eta$ (/s)\")\n", "plt.colorbar()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-59.5876106936\n", "0.457047855389\n" ] }, { "data": { "image/png": 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XJm6e6LBrFCwIf/5pNUvr1ctaUSQ8j6y6EQ91/Mpxqk6oyuGhh8mR0fPbJGoNgwfDunXw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\nlH+4c8fqMT9yJFS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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "wt = np.arange(-np.pi,np.pi,0.01)\n", "AK = 2/3.\n", "BK = 0.42\n", "phi = 2.18\n", "eta = (AK-BK)*np.cos(wt) + 2*BK * np.cos(wt-phi/2.) * np.cos(phi/2.)\n", "u = (AK-BK)*np.cos(wt) - 2*BK * np.sin(wt-phi/2.) * np.sin(phi/2.)\n", "plt.plot(wt,eta)\n", "plt.plot(wt,u)\n", "print ((wt[np.argmax(u)])-(wt[np.argmax(eta)]))*180./np.pi\n", "print ((u[np.argmax(u)])/(eta[np.argmax(eta)]))*g/c" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(30, 629, 23) (30, 629, 23) (30,)\n", "[ 0. 0.329]\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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NSUciIpIOTf3bgkU1rRzP6lJWUvZleqkpoakCXqULa8axdklzQ7Bo5PptRd/1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "swt = np.arange(-np.pi,np.pi,0.01)\n", "AK = 2/3.\n", "sBK = 1/3.+np.arange(-0.15,0.15,0.01)\n", "sphi = np.arange(0,2.3,0.1)*np.pi\n", "wt, BK, phi = np.meshgrid(swt, sBK, sphi)\n", "eta = (AK-BK)*np.cos(wt) + 2*BK * np.cos(wt-phi/2.) * np.cos(phi/2.)\n", "u = (AK-BK)*np.cos(wt) - 2*BK * np.sin(wt-phi/2.) * np.sin(phi/2.)\n", "#plt.plot(wt,eta)\n", "#plt.plot(wt,u)\n", "phase = np.zeros((u.shape[0],u.shape[2]))\n", "amp = np.zeros_like(phase)\n", "print u.shape, eta.shape, sBK.shape\n", "for i, Bs in enumerate(sBK):\n", " for j, Ps in enumerate(sphi):\n", " phase[i,j] = ((wt[i,np.argmax(u[i,:,j]),j])-(wt[i,np.argmax(eta[i,:,j]),j]))*180./np.pi\n", " amp[i,j] = ((u[i,np.argmax(u[i,:,j]),j])/(eta[i,np.argmax(eta[i,:,j]),j]))*g/c\n", "plt.figure(figsize=(14,7))\n", "plt.subplot(1,2,1)\n", "plt.contourf(sphi,sBK,phase)\n", "plt.colorbar()\n", "levels1 = np.arange(0.,2*0.329,0.329)\n", "plt.contour(sphi, sBK, amp, levels1)\n", "plt.xlabel(\"Intrinsic Phase Shift Between In and Out Wave\")\n", "plt.ylabel(\"Strength of Out Wave (in wave = 0.67)\")\n", "plt.title(\"Observed Phase Shift Between u and $\\eta$\")\n", "levels2 = np.arange(0.,2.*54,54.)\n", "print levels1\n", "plt.contour(sphi, sBK, phase, levels2)\n", "plt.plot(4.41,0.348,'*w')\n", "plt.subplot(1,2,2)\n", "plt.contourf(sphi,sBK,amp)\n", "plt.xlabel(\"Intrinsic Phase Shift Between In and Out Wave\")\n", "plt.ylabel(\"Strength of Out Wave (in wave = 0.67)\")\n", "plt.title(\"Observed Amplitude Ratio Between u and $\\eta$ (/s)\")\n", "plt.xlim((4,5))\n", "plt.colorbar()\n", "plt.plot(4.41,0.348,'*w')\n", "plt.contour(sphi, sBK, amp, levels1)\n", "plt.contour(sphi, sBK, phase, levels2)\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "54.4309905374\n", "0.331337914179\n" ] }, { "data": { "image/png": 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Jona+2nYCPIPWrc02ED3szvx8ZmmTpKVN8TZ89dtXtqOIWCI9ehElWpvx5hdegNGj7WQI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\nfpISk0uw4sMVFHmhiJU/Q0x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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "wt = np.arange(-np.pi,np.pi,0.05)\n", "AK = 2/3.\n", "BK = 0.348\n", "phi = 4.41\n", "eta = (AK-BK)*np.cos(wt) + 2*BK * np.cos(wt-phi/2.) * np.cos(phi/2.)\n", "u = (AK-BK)*np.cos(wt) - 2*BK * np.sin(wt-phi/2.) * np.sin(phi/2.)\n", "plt.plot(wt,eta)\n", "plt.plot(wt,u)\n", "print ((wt[np.argmax(u)])-(wt[np.argmax(eta)]))*180./np.pi\n", "print ((u[np.argmax(u)])/(eta[np.argmax(eta)]))*g/c" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "5.74619099535e-06\n", "164017.833177\n" ] } ], "source": [ "omega = 2*np.pi/(12.4*3600.) \n", "cm = np.sqrt(g*60.)\n", "k = omega/cm\n", "print k\n", "phi = 0.6*np.pi\n", "print phi/k/2." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2.9688653476e-06\n", "158726.935332\n" ] } ], "source": [ "omega = 2*np.pi/(24.*3600.) \n", "cm = np.sqrt(g*60.)\n", "k = omega/cm\n", "print k\n", "phi = 0.3*np.pi\n", "print phi/k/2." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "22.91898774470794" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "0.4/3.1415*180" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "1.8599999999999999" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "54/360.*12.4" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "3.1" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "90./360.*12.4" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.59375" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "0.19/0.32" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.7027027027027027" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "0.26/0.37" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }