Matlab help: inverting the linear water
waves dispersion relation
J. Rabault
9th February 2016
Here is a little example of how to use the fsolve Matlab function to numerically inverse the
dispersion relation for deep water waves: ω 2 = g.k.tanh(kh). The following code should be
run from a script:
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clear all;
close all;
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%% global parameters
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g = 9.81;
h = 0.7;
% water depth
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% suppressing text output from fsolve
% note: this is dangerous, only if sure of what I do...
options = optimset('Display','off');
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%% compute the angular frequency, wave number, wave length from frequency
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fprintf('Condition is imposed frequency: ');
fprintf('\n');
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frequency = 1.5;
omega = 2*pi*frequency;
% frequency in Hertz
% angular frequency rad / s
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% compute the wave number from dispersion relation
% global variables are temporarily used to pass arguments
global gGlobal;
global hGlobal;
global omegaGlobal;
gGlobal = g;
hGlobal = h;
omegaGlobal = omega;
[k]=fsolve(@DispersionRelationWithArgs,1,options);
clear gGlobal;
clear hGlobal;
clear omegaGlobal;
lambda = 2*pi/k;
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fprintf('wave length lambda (m) %d',lambda);
fprintf('\n');
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Matlab help: fsolve
And you should have in the same folder a function called DispersionRelationWithArgs,
containing the following code:
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function [ OmegaRes ] = DispersionRelationWithArgs(k)
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global gGlobal;
global hGlobal;
global omegaGlobal;
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% Dispersion relation for linear waves
% g and h are given as global variables (for inverse
% problem solving with only one argument).
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%
%
%
%
OmegaRes the residual to make equal to zero
omegaGlobal the omega for which k should be computed
k the wave number
gGlobal, hGlobal given as global
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OmegaRes = sqrt(gGlobal*k*tanh(k*hGlobal))-omegaGlobal;
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end
J. Rabault
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