| 1 | """Example of shallow water wave equation. |
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| 2 | |
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| 3 | Flat bed with rotational wind stress |
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| 4 | |
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| 5 | """ |
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| 6 | |
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| 7 | ###################### |
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| 8 | # Module imports |
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| 9 | # |
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| 10 | from mesh_factory import rectangular |
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| 11 | from shallow_water import Domain, Reflective_boundary, Wind_stress |
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| 12 | |
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| 13 | #Create basic mesh |
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| 14 | N = 80 |
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| 15 | len = 100 |
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| 16 | points, vertices, boundary = rectangular(N, N, len, len) |
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| 17 | |
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| 18 | #Create shallow water domain |
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| 19 | domain = Domain(points, vertices, boundary) |
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| 20 | domain.smooth = True |
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| 21 | domain.visualise = False |
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| 22 | domain.store = True |
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| 23 | domain.default_order=2 |
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| 24 | domain.set_name('wind_rotation') |
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| 25 | |
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| 26 | #Set initial conditions |
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| 27 | domain.set_quantity('elevation', 0.0) |
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| 28 | domain.set_quantity('level', 2.0) |
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| 29 | domain.set_quantity('friction', 0.0) |
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| 30 | |
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| 31 | |
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| 32 | #Variable windfield implemented using functions |
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| 33 | def speed(x,y,t): |
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| 34 | """Large speeds halfway between center and edges |
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| 35 | Low speeds at center and edges |
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| 36 | """ |
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| 37 | |
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| 38 | from math import sqrt, exp, cos, pi |
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| 39 | |
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| 40 | c = (len1/2, len2/2) |
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| 41 | r = sqrt((x - c[0])**2 + (y - c[1])**2) |
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| 42 | |
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| 43 | r /= max(len1,len2) |
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| 44 | |
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| 45 | factor = exp( -(r-0.15)**2 ) |
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| 46 | |
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| 47 | #print x,y,factor |
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| 48 | |
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| 49 | return 4000 * factor * (cos(t*2*pi/150) + 2) |
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| 50 | |
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| 51 | |
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| 52 | def phi(x,y,t): |
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| 53 | """Rotating field |
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| 54 | """ |
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| 55 | from math import sqrt, atan, pi |
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| 56 | |
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| 57 | c = (len1/2, len2/2) |
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| 58 | r = sqrt((x - c[0])**2 + (y - c[1])**2) |
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| 59 | |
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| 60 | xx = (x - c[0])/len1 |
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| 61 | yy = (y - c[1])/len2 |
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| 62 | |
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| 63 | angle = atan(yy/xx) |
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| 64 | |
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| 65 | if xx < 0: |
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| 66 | angle+=pi #atan in ]-pi/2; pi/2[ |
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| 67 | |
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| 68 | #Take normal direction |
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| 69 | angle -= pi/2 |
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| 70 | |
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| 71 | #Ensure positive radians |
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| 72 | if angle < 0: |
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| 73 | angle += 2*pi |
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| 74 | |
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| 75 | return angle/pi*180 |
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| 76 | |
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| 77 | |
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| 78 | domain.forcing_terms.append( Wind_stress(speed, phi) ) |
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| 79 | |
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| 80 | |
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| 81 | #Add lateral wind gusts bearing 25 deg |
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| 82 | def gust(x,y,t): |
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| 83 | from math import sin, pi |
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| 84 | |
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| 85 | tt = sin(2*pi*t/200) |
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| 86 | |
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| 87 | if tt > 0.9: |
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| 88 | return 6000*tt |
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| 89 | else: |
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| 90 | return 0 |
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| 91 | |
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| 92 | domain.forcing_terms.append(Wind_stress(gust, 25)) |
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| 93 | |
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| 94 | |
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| 95 | ###################### |
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| 96 | # Boundary conditions |
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| 97 | Br = Reflective_boundary(domain) |
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| 98 | domain.set_boundary({'left': Br, 'right': Br, 'top': Br, 'bottom': Br}) |
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| 99 | |
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| 100 | ###################### |
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| 101 | #Evolution |
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| 102 | for t in domain.evolve(yieldstep = 0.5, finaltime = 1000): |
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| 103 | domain.write_time() |
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| 104 | |
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| 105 | print 'Done' |
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| 106 | |
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