{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 83, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 83, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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b7QvkzVpXF0tO+anMos71f6rp9XSBL5oS1ICCztx6umkOyQu7Vv9GJwOn/tLE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\n4arPzAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.arange(0,2*np.pi,0.1)\n", "t = np.arange(0,2*np.pi,0.1)\n", "xf, tf = np.meshgrid(x,t)\n", "\n", "eta1 = -np.cos(xf)*np.sin(-tf)\n", "eta2 = np.sin(xf-tf)\n", "\n", "plt.figure(figsize=(15,5))\n", "plt.subplot(1,3,1)\n", "plt.contourf(x,t,eta1)\n", "plt.xlabel('Distance')\n", "plt.ylabel('Time')\n", "plt.colorbar()\n", "plt.subplot(1,3,2)\n", "plt.contourf(x,t,eta2)\n", "plt.xlabel('Distance')\n", "plt.ylabel('Time')\n", "plt.colorbar()\n", "plt.subplot(1,3,3)\n", "plt.contourf(x,t,eta1+eta2)\n", "plt.xlabel('Distance')\n", "plt.ylabel('Time')\n", "plt.colorbar()" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(571.93230704341227, 'maximum variation distance in km')\n" ] } ], "source": [ "c = np.sqrt(67 * 9.8)\n", "omega = 2 * np.pi / (12.4*3600.)\n", "ke = omega / c\n", "lamb = 2 * np.pi / ke\n", "print (lamb/2./1000, 'maximum variation distance in km')" ] }, { "cell_type": "code", "execution_count": 177, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 177, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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axa/E65g1YO4InaRDJb1a0jmSdki6rvz91ZIOaSvIJiVPSmbWKWefmjqChiUc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\nWaDv9OhF2t1t9dD6oxPF3Ak4QfWF/5f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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "L = 400e3\n", "x = np.arange(0,L*1.02,0.02*L)\n", "t = np.arange(0,2*np.pi,0.02) / omega\n", "Kappa = 0.29 * omega\n", "xf, tf = np.meshgrid(x,t)\n", "eta = (-np.cos(ke * xf) * np.sin(-omega * tf) + np.sin(ke * xf - omega * tf)) * np.exp(- Kappa * xf / (2*c))\n", "etaimage = (( - np.cos(ke * (2*L - xf)) * np.sin(- omega * tf)\n", " + sin(ke *(2*L - xf) - omega * tf) )\n", " * np.exp(- Kappa * (2*L - xf) / (2*c)) )\n", "etaimage2 = (( -np.cos(ke * (2*L + xf)) * np.sin(-omega * tf)\n", " + sin(ke * (2*L + xf) - omega * tf) )\n", " * np.exp(- Kappa * (2*L + xf) / (2*c)) )\n", "plt.figure(figsize=(15,5))\n", "plt.subplot(1,3,1)\n", "plt.contourf(x/1000., t/3600., eta)\n", "plt.xlabel('Distance (km)')\n", "plt.ylabel('Time (hr)')\n", "plt.colorbar()\n", "plt.subplot(1,3,2)\n", "plt.contourf(xf/1000., tf/3600., etaimage)\n", "plt.colorbar()\n", "plt.subplot(1,3,3)\n", "plt.contourf(xf/1000., tf/3660., eta + etaimage - etaimage2)\n", "plt.colorbar()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Maximum impact in at head of domain.\n", "\n", "Note that it is completely a standing wave. " ] }, { "cell_type": "code", "execution_count": 245, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 80 82 84 86 88 91 94 98 102 106 111 117 123 129 136 143 150 157\n", " 162 168 173 177 180 184 187 189 191 193 195 197 199 200 201 203 204 205\n", " 206 207 208 209 209 210 211 212 212 213 214 215 215 216 217]\n", "0.705687782465\n", "21.772396215\n", "1.05143236232 -9.16732472209\n" ] }, { "data": { "image/png": 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ejhPzuUqs9/pZlR0iYfmTIX+K6Sns43TZG0Wwwj0S+vt/pV6zRSD49yLgkozPlRJbdvWk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\nLQGOcvfZZrYWcJeZ3ezu8wL0pbKDJxEZSPd8qkGhJ5HS2b0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.arange(0,L*1.02,0.02*L)\n", "t = np.arange(0,2*np.pi,0.02) / omega\n", "xf, tf = np.meshgrid(x,t)\n", "phase = 1.32*np.pi\n", "Ak = 0.67*cos(ke*xf - omega*tf - phase)\n", "Bk = 0.35*cos(-ke*xf - omega*tf + 2*ke*L - phase)\n", "plt.figure(figsize=(15,5))\n", "plt.subplot(1,3,1)\n", "plt.contourf(x/1000., t/3600., Ak+Bk)\n", "themax = np.argmax(Ak+Bk,axis=0)\n", "\n", "plt.plot(x/1000.,t[themax]/3600.)\n", "print (themax)\n", "plt.xlabel('Distance (km)')\n", "plt.ylabel('Time (hr)')\n", "plt.colorbar()\n", "plt.subplot(1,3,2)\n", "total = (Ak+Bk +0.16*(eta + etaimage - etaimage2)) \n", "scale = np.max(Ak+Bk)/np.max(total)\n", "total = total *scale\n", "plt.contourf(x/1000., t/3600., total)\n", "themax2 = np.argmax(total,axis=0)\n", "plt.plot(x/1000.,t[themax]/3600.)\n", "plt.plot(x/1000.,t[themax2]/3600.)\n", "plt.plot(x/1000.,(t[themax2]+t[themax[-1]]-t[themax2[-1]])/3600.)\n", "plt.xlabel('Distance (km)')\n", "plt.ylabel('Time (hr)')\n", "plt.colorbar()\n", "plt.subplot(1,3,3)\n", "plt.contourf(x/1000., t/3600., 0.16*(eta + etaimage - etaimage2) *scale)\n", "plt.xlabel('Distance (km)')\n", "plt.ylabel('Time (hr)')\n", "plt.colorbar()\n", "print np.min(np.max(total, axis = 0))/ np.min(np.max(Ak+Bk, axis = 0))\n", "print np.max(t[themax]-t[themax2]-t[themax[-1]]+t[themax2[-1]])*360./(12.4*3600.)\n", "print scale, (t[themax[-1]]-t[themax2[-1]])*360./(12.4*3600.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "phase = -0.4 pi and amp = -0.4: phase lates in center, so phase change between \"victoria\" and \"pt atkinson\" too low, amphidrome too deep \n", "phase = -0.4 pi and amp = 0.4: phase early in center, total phase change too big, amphidrome too early\n", "\n", "This suggests flux is too little. Maximum in eta is at 1.5 hours, maximum u is 54 degrees or 1.85 hours later, and eta follows u by 90o, 3.1 hours for a standing wave. So pushing in u should give a maximum in eta at 6.75 hours, but what I have is a minimum. So I need more flux!\n", "\n", "phase = -0.4 pi and amp = 0.1: phase difference better, but amphidrome too full \n", "phase = -0.6 pi and amp = 0.1: phase difference good, amphidrome too deep \n", "phase = -0.6 pi and amp = 0.2: phase difference good (max 15o) amphidrome a bit too much too deep (60% rather than 70%) \n", "phase = -1.32 pi and amp = 0.16 phase difference good (max 21o) amphidrome good\n", "\n", "Maximum eta is now at 3 hours, maximum u is 1.85 hours later and eta follows u by 3.1 hours. So pushing u should give a maximum in eta at 7.95 hours, 8 hours. I have a minimum at 6.2 hours." ] }, { "cell_type": "code", "execution_count": 228, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 228, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(x/1000.,(t[themax]-t[themax2]-t[themax[-1]]+t[themax2[-1]])*360./(12.4*3600.))" ] }, { "cell_type": "code", "execution_count": 253, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0.68524343 0.6530001 0.61996811 0.5862851 0.55211999 0.51766035\n", " 0.4831435 0.44888024 0.41521021 0.38258083 0.35161104 0.32301109\n", " 0.29772823 0.27689303 0.26174483 0.25341958 0.25267243 0.25956069\n", " 0.27344544 0.29325113 0.31771712 0.34568161 0.37615924 0.40840789\n", " 0.44177474 0.47583729 0.51016528 0.54450123 0.57856559 0.61221291\n", " 0.64519996 0.67744284 0.70876157 0.73905992 0.76824506 0.79622787\n", " 0.82292334 0.84825084 0.87213443 0.89450315 0.91531657 0.9345704\n", " 0.95214158 0.96797984 0.98216985 0.99455859 1.00512688 1.01395934\n", " 1.02090759 1.02603057 1.02932616]\n", "[ 0.68524343 0.65290369 0.61965011 0.58565218 0.55101777 0.51595119\n", " 0.48063477 0.44531231 0.41035437 0.37610454 0.34311519 0.31208552\n", " 0.28391875 0.25979734 0.2411511 0.22947016 0.22594349 0.23095722\n", " 0.24393166 0.26360902 0.28848444 0.3171484 0.34847363 0.38160213\n", " 0.41584425 0.45075048 0.48588107 0.5209821 0.55579429 0.59013666\n", " 0.62379242 0.65667369 0.68864299 0.71957368 0.7493723 0.77794936\n", " 0.80521965 0.83111571 0.85561511 0.8785976 0.89999659 0.91980915\n", " 0.93799417 0.95444142 0.9691995 0.98219688 0.99335834 1.00279729\n", " 1.0103453 1.01608689 1.01997819]\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.contourf(x/1000., t/3600., total - 0.25*(eta + etaimage - etaimage2)*cos(2.8*3600.*omega))\n", "plt.plot(x/1000.,t[themax2]/3600.)\n", "plt.colorbar()\n", "print np.max(total - 0.25*(eta + etaimage - etaimage2)*cos(2.8*3600.*omega), axis = 0)\n", "print np.max(total, axis=0)" ] }, { "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 }