wavenumber.m

Solves the wave dispersion relation using the Newton-Raphson method including currents

Solves the wave dispersion relation
sig^2 = g*wk*tanh(wk*h)
where
g = gravity [L/T^2]
h = water depth [L]
sig = Relative angular frequency [rad/T]
sig = wa - wk*cos(wd)*u - wk*cos(wd)*v = wa - wk*uk [rad/T]
uk = cos(wd)*u + sin(wd)*v [L/T]
u = current velocity in x direction [L/T]
v = current velocity in y direction [L/T]

The Newton-Raphson Method is given by
wk(n+1) = wk(n) - f(k(n))/fp(k(n))
where
f = g*wk*tanh(wk*h) - sig^2
fp = g*(tanh(wk*h) - h*wk*(tanh(wk*h)^2-1)) + 2*uk*sig

Makes initial guess using
Guo, J. (2002) Simple and explicit solution of wave dispersion, Coastal Engineering, 46(2), 71-74.
A simple correction is applied to the initial guess to account for for currents.