{ "cells": [ { "cell_type": "markdown", "id": "graphic-vietnam", "metadata": {}, "source": [ "# Surface waves" ] }, { "cell_type": "code", "execution_count": 1, "id": "false-owner", "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "%config InlineBackend.figure_format = 'svg'\n", "import numpy as np\n", "#import matplotlib.pyplot as plt\n", "from matplotlib import pyplot as plt, animation\n", "from matplotlib.gridspec import GridSpec #for multiple sub(plots)\n", "#plt.style.use('ggplot') #plotting style like in R\n", "import matplotlib.animation\n", "from IPython.display import display, clear_output" ] }, { "cell_type": "code", "execution_count": 2, "id": "middle-guitar", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "102" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pi = np.pi\n", "#x = np.linspace(0,2*pi,100)\n", "t = np.arange(0,51,0.5) #0:512;\n", "x = np.arange(0,2*pi,0.1) #0:0.1:2*pi;\n", "#XX, YY = np.meshgrid(xx,yy) \n", "k=2.0 #wavenumber\n", "amp = 0.2 #amplitude\n", "lam = 2.0*pi/k #lambda-> wavelength\n", "g = 9.8 #m/s\n", "H = 0.65*lam #m \n", "#\n", "omg = np.sqrt(g*k*np.tanh(k*H))\n", "omg1 = omg # used to change direction of propagation\n", "#\n", "Lx = np.size(x) #length(x);\n", "Lt = np.size(t) #length(t);\n", "#\n", "eta = np.zeros((Lx,Lt))\n", "Lt" ] }, { "cell_type": "code", "execution_count": 3, "id": "tribal-letter", "metadata": {}, "outputs": [], "source": [ "for ii in range(0,Lx): #ii = 1:Lx\n", " for m in range(0,Lt): #m = 1:length(t)\n", " eta[ii,m] = amp*np.cos(k*x[ii]-omg1*t[m]) # amp*cosf(i,m)\n", " #print(amp*np.cos(k*x[ii]-omg*t[m])) \n", " #print(eta[ii,m])\n", " \n", "# fig, ax = plt.subplots(figsize=(5,3))\n", "# tm=0\n", "# ax.plot(x,eta[:,tm],color='black',linestyle='-')\n", "# tm=10\n", "# ax.plot(x,eta[:,tm],color='red',linestyle='-')\n", "# tm=20\n", "# ax.plot(x,eta[:,tm],color='blue',linestyle='-')\n", "# plt.xlim(0, x[-1])\n", "# plt.ylim(-H,np.max(np.max(eta)))" ] }, { "cell_type": "code", "execution_count": 4, "id": "radio-breakfast", "metadata": {}, "outputs": [], "source": [ "z = np.arange(-H,np.max(np.max(eta)),0.05) #-H:0.05:max(max(eta))\n", "Lz = np.size(z) #length(z)\n", "\n", "phi = np.zeros((Lx,Lz,Lt)) #zeros(Lx,Lz,Lt)\n", "U = np.zeros((Lx,Lz,Lt)) #zeros(Lx,Lz,Lt)\n", "W = np.zeros((Lx,Lz,Lt)) #zeros(Lx,Lz,Lt)" ] }, { "cell_type": "code", "execution_count": 5, "id": "breeding-liquid", "metadata": {}, "outputs": [], "source": [ "for m in range(0,Lt): #1:Lt\n", " for ii in range(0,Lx): #1:Lx\n", " for jj in range(0,Lz): #jj=1:Lz\n", " phi[ii,jj,m] =((amp*omg/k)*np.cosh(k*(z[jj]+H))/(np.sinh(k*H)))*np.sin(k*x[ii]-omg1*t[m])\n", " U[ii,jj,m] =(amp*omg*np.cosh(k*(z[jj]+H))/(np.sinh(k*H)))*np.cos(k*x[ii]-omg1*t[m])\n", " W[ii,jj,m] =(amp*omg*np.sinh(k*(z[jj]+H))/(np.sinh(k*H)))*np.sin(k*x[ii]-omg1*t[m]) \n", " " ] }, { "cell_type": "code", "execution_count": 6, "id": "qualified-enough", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\r\n", "\r\n", "\r\n", "\r\n" ], "text/plain": [ "

" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#This cell takes a while to execute\n", "tm = 5\n", "UU = np.transpose(U[:,:,tm]) #squeeze(U(:,:,tm))'\n", "WW = np.transpose(W[:,:,tm]) #squeeze(W(:,:,tm))'\n", "PP = np.transpose(phi[:,:,tm])\n", "##Plot contour\n", "fig, ax = plt.subplots(figsize=(5,3))\n", "xc=plt.contourf(x, z, WW, 16,cmap='jet') #RdGy -> Red-Grey colormap\n", "plt.colorbar()\n", "#fig.colorbar(xc,ax)\n", "##Plot eta -- displacement\n", "ax.plot(x,eta[:,tm],color='black',linestyle='-')\n", "plt.xlim(0, x[-1])\n", "plt.ylim(-H,np.max(np.max(eta)))\n", "ax.set_xlabel('$x$', color='k')\n", "ax.set_ylabel('Height', color='k')\n", " \n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 7, "id": "classified-peeing", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\r\n", "\r\n", "\r\n", "\r\n" ], "text/plain": [ "

" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(2,2,figsize=(8, 6), sharex=True, sharey=False)\n", "## Set the title for the figure\n", "# fig.suptitle('This is the Figure Title', fontsize=15)\n", "## Top Left Subplot\n", "eta1, =axes[0,0].plot(x,eta[:,tm],color='blue',linestyle='-')\n", "u1, =axes[0,0].plot(x,U[:,20,tm],color='red',linestyle='-')\n", "w1, =axes[0,0].plot(x,W[:,20,tm],color='black',linestyle='-')\n", "axes[0,0].axhline(y=0,color='black',lw=0.5,linestyle='--')#or with x-range\n", "#axes[0,0].set_title('$\\phi$')\n", "axes[0,0].legend((eta1,u1,w1), ('$\\eta$', '$u$','$w$'))\n", "#axes[0,0].text(0.5, 0.5, 'matplotlib', horizontalalignment='center',\n", "# verticalalignment='center', transform=ax.transAxes)\n", "#\n", "img1 = axes[0,1].contourf(x, z,PP, 16,cmap='jet')\n", "axes[0,1].set_title('$\\phi$')\n", "axes[0,1].set_ylabel('$z$')\n", "ax=axes[0,1]\n", "fig.colorbar(img1,ax=ax,orientation='vertical')\n", "## Top Right Subplot\n", "img2=axes[1,0].contourf(x, z, UU, 16,cmap='jet')\n", "axes[1,0].set_title('$u$')\n", "axes[1,0].set_xlabel('$x$')\n", "axes[1,0].set_ylabel('$z$')\n", "ax=axes[1,0]\n", "fig.colorbar(img2,ax=ax,orientation='vertical')\n", "# # Bottom Right Subplot\n", "img3=axes[1,1].contourf(x, z, WW, 16,cmap='jet')\n", "axes[1,1].set_title('$w$')\n", "axes[1,1].set_xlabel('$x$')\n", "ax=axes[1,1]\n", "fig.colorbar(img3,ax=ax,orientation='vertical')\n", "#labels\n", "axes[0,0].text(0.1, 0.23, '(a)',fontsize=12)\n", "axes[0,1].text(0.1, 0.23, '(b)',fontsize=12)\n", "axes[1,0].text(0.1, 0.23, '(c)',fontsize=12)\n", "axes[1,1].text(0.1, 0.23, '(d)',fontsize=12)\n", "#\n", "dirpath ='C:/Users/Owner/Documents/University_of_Ghana/DeptOfMath/Teaching/LECTURE_NOTES/Water_waves/figures/'\n", "#plt.savefig(dirpath + 'figure_sw1.pdf')\n", "##plt.savefig('figure_sw1.pdf')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 9, "id": "adjustable-scanner", "metadata": {}, "outputs": [ { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", "window.mpl = {};\n", "\n", "\n", "mpl.get_websocket_type = function() {\n", " if (typeof(WebSocket) !== 'undefined') {\n", " return WebSocket;\n", " } else if (typeof(MozWebSocket) !== 'undefined') {\n", " return MozWebSocket;\n", " } else {\n", " alert('Your browser does not have WebSocket support.' +\n", " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", " 'Firefox 4 and 5 are also supported but you ' +\n", " 'have to enable WebSockets in about:config.');\n", " };\n", "}\n", "\n", "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", " this.id = figure_id;\n", "\n", " this.ws = websocket;\n", "\n", " this.supports_binary = (this.ws.binaryType != undefined);\n", "\n", " if (!this.supports_binary) {\n", " var warnings = document.getElementById(\"mpl-warnings\");\n", " if (warnings) {\n", " warnings.style.display = 'block';\n", " warnings.textContent = (\n", " \"This browser does not support binary websocket messages. \" +\n", " \"Performance may be slow.\");\n", " }\n", " }\n", "\n", " this.imageObj = new Image();\n", "\n", " this.context = undefined;\n", " this.message = undefined;\n", " this.canvas = undefined;\n", " this.rubberband_canvas = undefined;\n", " this.rubberband_context = undefined;\n", " this.format_dropdown = undefined;\n", "\n", " this.image_mode = 'full';\n", "\n", " this.root = $('

');\n", " this._root_extra_style(this.root)\n", " this.root.attr('style', 'display: inline-block');\n", "\n", " $(parent_element).append(this.root);\n", "\n", " this._init_header(this);\n", " this._init_canvas(this);\n", " this._init_toolbar(this);\n", "\n", " var fig = this;\n", "\n", " this.waiting = false;\n", "\n", " this.ws.onopen = function () {\n", " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", " fig.send_message(\"send_image_mode\", {});\n", " if (mpl.ratio != 1) {\n", " fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n", " }\n", " fig.send_message(\"refresh\", {});\n", " }\n", "\n", " this.imageObj.onload = function() {\n", " if (fig.image_mode == 'full') {\n", " // Full images could contain transparency (where diff images\n", " // almost always do), so we need to clear the canvas so that\n", " // there is no ghosting.\n", " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", " }\n", " fig.context.drawImage(fig.imageObj, 0, 0);\n", " };\n", "\n", " this.imageObj.onunload = function() {\n", " fig.ws.close();\n", " }\n", "\n", " this.ws.onmessage = this._make_on_message_function(this);\n", "\n", " this.ondownload = ondownload;\n", "}\n", "\n", "mpl.figure.prototype._init_header = function() {\n", " var titlebar = $(\n", " '

');\n", " var titletext = $(\n", " '

');\n", " titlebar.append(titletext)\n", " this.root.append(titlebar);\n", " this.header = titletext[0];\n", "}\n", "\n", "\n", "\n", "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", "\n", "}\n", "\n", "\n", "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", "\n", "}\n", "\n", "mpl.figure.prototype._init_canvas = function() {\n", " var fig = this;\n", "\n", " var canvas_div = $('

');\n", "\n", " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", "\n", " function canvas_keyboard_event(event) {\n", " return fig.key_event(event, event['data']);\n", " }\n", "\n", " canvas_div.keydown('key_press', canvas_keyboard_event);\n", " canvas_div.keyup('key_release', canvas_keyboard_event);\n", " this.canvas_div = canvas_div\n", " this._canvas_extra_style(canvas_div)\n", " this.root.append(canvas_div);\n", "\n", " var canvas = $('