1 | """ |
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2 | This module contains various auxiliary function used |
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3 | to ascertain wet dry areas. |
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4 | """ |
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5 | |
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6 | |
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7 | import numpy |
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8 | |
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9 | def calculate_wetted_area(x1,x2,z1,z2,w1,w2): |
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10 | if (w1 > z1) & (w2 < z2) & (z1 <= z2): |
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11 | x = ((w2-z1)*(x2-x1)+x1*(z2-z1)-x2*(w2-w1))/(z2-z1+w1-w2) |
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12 | A = 0.5*(w1-z1)*(x-x1) |
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13 | L = x-x1 |
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14 | elif (w1 < z1) & (w2 > z2) & (z1 < z2): |
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15 | x = ((w2-z1)*(x2-x1)+x1*(z2-z1)-x2*(w2-w1))/(z2-z1+w1-w2) |
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16 | A = 0.5*(w2-z2)*(x2-x) |
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17 | L = x2-x |
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18 | elif (w1 < z1) & (w2 > z2) & (z1 >= z2): |
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19 | x = ((w1-z2)*(x2-x1)+x2*(z2-z1)-x1*(w2-w1))/(z2-z1+w1-w2) |
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20 | A = 0.5*(w2-z2)*(x2-x) |
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21 | L = x2-x |
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22 | elif (w1 > z1) & (w2 < z2) & (z1 > z2): |
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23 | x = ((w1-z2)*(x2-x1)+x2*(z2-z1)-x1*(w2-w1))/(z2-z1+w1-w2) |
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24 | A = 0.5*(w1-z1)*(x-x1) |
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25 | L = x-x1 |
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26 | elif (w1 <= z1) & (w2 <= z2): |
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27 | A = 0.0 |
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28 | elif (w1 == z1) & (w2 > z2) & (z2 < z1): |
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29 | A = 0.5*(x2-x1)*(w2-z2) |
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30 | elif (w2 == z2) & (w1 > z1) & (z1 < z2): |
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31 | A = 0.5*(x2-x1)*(w1-z1) |
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32 | return A |
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33 | |
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34 | |
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35 | def calculate_new_wet_area(x1,x2,z1,z2,A): |
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36 | from numpy import sqrt |
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37 | min_centroid_height = 1.0e-3 |
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38 | # Assumes reconstructed stage flat in a wetted cell |
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39 | M = (z2-z1)/(x2-x1) |
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40 | L = (x2-x1) |
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41 | min_area = min_centroid_height*L |
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42 | max_area = 0.5*(x2-x1)*abs(z2-z1) |
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43 | if A < max_area: |
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44 | if (z1 < z2): |
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45 | x = sqrt(2*A/M)+x1 |
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46 | wet_len = x-x1 |
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47 | wc = z1 + sqrt(M*2*A) |
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48 | elif (z2 < z1): |
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49 | x = -sqrt(-2*A/M)+x2 |
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50 | wet_len = x2-x |
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51 | wc = z2+sqrt(-M*2*A) |
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52 | else: |
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53 | wc = A/L+0.5*(z1+z2) |
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54 | wet_len = x2-x1 |
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55 | else: |
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56 | wc = 0.5*(z1+z2)+A/L |
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57 | wet_len = x2-x1 |
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58 | |
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59 | return wc,wet_len |
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60 | |
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61 | def calculate_new_wet_area_analytic(x1,x2,z1,z2,A,t): |
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62 | min_centroid_height = 1.0e-3 |
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63 | # Assumes reconstructed stage flat in a wetted cell |
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64 | M = (z2-z1)/(x2-x1) |
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65 | L = (x2-x1) |
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66 | min_area = min_centroid_height*L |
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67 | max_area = 0.5*(x2-x1)*abs(z2-z1) |
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68 | w1,uh1 = analytic_cannal(x1,t) |
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69 | w2,uh2 = analytic_cannal(x2,t) |
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70 | if (w1 > z1) & (w2 < z2) & (z1 <= z2): |
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71 | print "test1" |
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72 | x = ((w2-z1)*(x2-x1)+x1*(z2-z1)-x2*(w2-w1))/(z2-z1+w1-w2) |
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73 | wet_len = x-x1 |
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74 | elif (w1 < z1) & (w2 > z2) & (z1 < z2): |
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75 | print "test2" |
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76 | x = ((w2-z1)*(x2-x1)+x1*(z2-z1)-x2*(w2-w1))/(z2-z1+w1-w2) |
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77 | wet_len = x2-x |
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78 | elif (w1 < z1) & (w2 > z2) & (z1 >= z2): |
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79 | print "test3" |
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80 | x = ((w1-z2)*(x2-x1)+x2*(z2-z1)-x1*(w2-w1))/(z2-z1+w1-w2) |
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81 | wet_len = x2-x |
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82 | elif (w1 > z1) & (w2 < z2) & (z1 > z2): |
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83 | print "test4" |
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84 | x = ((w1-z2)*(x2-x1)+x2*(z2-z1)-x1*(w2-w1))/(z2-z1+w1-w2) |
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85 | wet_len = x-x1 |
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86 | elif (w1 >= z1) & (w2 >= z2): |
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87 | print "test5" |
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88 | wet_len = x2-x1 |
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89 | else: #(w1 <= z1) & (w2 <= z2) |
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90 | print "test5" |
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91 | if (w1 > z1) | (w2 > z2): |
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92 | print "ERROR" |
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93 | wet_len = x2-x1 |
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94 | return w1,w2,wet_len,uh1,uh2 |
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95 | |
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96 | def analytic_cannal(C,t): |
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97 | |
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98 | import math |
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99 | #N = len(C) |
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100 | #u = zeros(N,numpy.float) ## water velocity |
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101 | #h = zeros(N,numpy.float) ## water depth |
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102 | x = C |
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103 | g = 9.81 |
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104 | |
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105 | |
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106 | ## Define Basin Bathymetry |
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107 | #z_b = zeros(N,numpy.float) ## elevation of basin |
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108 | #z = zeros(N,numpy.float) ## elevation of water surface |
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109 | z_infty = 10.0 ## max equilibrium water depth at lowest point. |
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110 | L_x = 2500.0 ## width of channel |
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111 | |
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112 | A0 = 0.5*L_x ## determines amplitudes of oscillations |
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113 | omega = math.sqrt(2*g*z_infty)/L_x ## angular frequency of osccilation |
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114 | |
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115 | x1 = A0*cos(omega*t)-L_x # left shoreline |
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116 | x2 = A0*cos(omega*t)+L_x # right shoreline |
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117 | if (x >=x1) & (x <= x2): |
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118 | z_b = z_infty*(x**2/L_x**2) ## or A0*cos(omega*t)\pmL_x |
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119 | u = -A0*omega*sin(omega*t) |
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120 | z = z_infty+2*A0*z_infty/L_x*cos(omega*t)*(x/L_x-0.5*A0/(L_x)*cos(omega*t)) |
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121 | else: |
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122 | z_b = z_infty*(x**2/L_x**2) |
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123 | u=0.0 |
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124 | z = z_b |
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125 | h = z-z_b |
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126 | return z,u*h |
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