qkhfs.m

function kh = qkhfs( w, h )
% QKHFS - Quick iterative calculation of kh in dispersion relationship
% kh = qkhf( w, h )
%
% Input:
%  w Angular wave frequency = 2*pi/T where T = wave period [1/s]
%  h Water depth [m]
% Returns:
%  kh = wavenumber * depth [ ]
% 
% Either w or h can be a vector, but not both.
% Hard-wired for MKS units.
% Orbital velocities from kh are accurate to 3e-12 !
%
% RL Soulsby (2006) "Simplified calculation of wave orbital velocities"
% HR Wallingford Report TR 155, February 2006
% Eqns. 12a - 14

% csherwood@usgs.gov
% Sept 10, 2006

g = 9.81;
x = w.^2*h./g;
y = sqrt(x) .* (x<1) + x.* (x>=1);
%this appalling bit of code is about 25% faster than a for loop
t = tanh( y );
y = y-( (y.*t -x)./(t+y.*(1-t.^2)));
t = tanh( y );
y = y-( (y.*t -x)./(t+y.*(1-t.^2)));
t = tanh( y );
y = y-( (y.*t -x)./(t+y.*(1-t.^2)));
kh=y;
return;