%pylab inline

import clawpack.visclaw.colormaps as C

theta = pi/8.  
h0 = 10.
grav = 9.81
c = sqrt(grav*h0)
width = 10.
L =  2*width*sin(theta) 
print "Wavelength in direction of wave propagation L = %g" % L
print "Linearized propagation speed (if A small relative to h0): c = %g" % c

def wave(x,y,t,A):
    eta0 = A[0]*sin(2*pi*(x*cos(theta) + y*sin(theta) - c*t)/L)
    eta1 = A[1]*sin(2*pi*(x*cos(theta) - y*sin(theta) - c*t)/L)
    h = h0 + eta0 + eta1
    u = sqrt(grav/h0) * (eta0 + eta1) * cos(theta)
    v = sqrt(grav/h0) * (eta0 - eta1) * sin(theta)
    return h,u,v


x = linspace(-20,20,201)
y = linspace(-width,width,101)
X,Y = meshgrid(x,y)

def plot_wave(t,A):
    h,u,v = wave(X,Y,t,A)
    pcolor(X,Y,h,cmap=C.blue_white_red)
    contour(X,Y,v,colors='k')
    title('t = %8.3f, pcolor=h, contours=v' % t)
    axis('scaled')

figure(figsize=(10,6))
subplot(121)
plot_wave(0,[1,0])
subplot(122)
plot_wave(0,[0,1])

plot_wave(0,[1,1])
figure()
plot_wave(0.5,[1,1])