Check factor of 2 in Waves/SWIFT_Stokes.m #55
Description
Code was revised in Mar 2021 to include factor of 2 at lines 176-183, however comparison to other published equations suggest this factor of 2 is not necessary. For example, see Equation 5 in this paper (https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2020MS002172) or Equation 9.9 in Fabrice's textbook (https://github.com/ardhuin/waves_in_geosciences/blob/main/part1and2.pdf).
Confusion may stem from the "2" in both the numerator and denominator of the integrand:
I.e., to match equations, a factor of "2" needs to be added to the denominator in lines 164-172.
SWIFT-codes/Waves/SWIFT_Stokes.m
Lines 156 to 184 in f07c03d
Here is a MATLAB test case using a portion of the code above (please double check). Using my own code (not shown), I calculate a value that is half of the value output by this code: a Stokes magnitude of 0.0219 compared to 0.0407 (differences may be due to dispersion calculation/numerical integration).
% test comparison of .m and .py stokes drift codes
energy = [0.00174398, 0.00273885, 0.00324009, 0.00126474, 0.004198 , ...
0.00838162, 0.00286359, 0.00393084, 0.00944725, 0.01648753, ...
0.02518561, 0.01375298, 0.01577215, 0.03096342, 0.05275692, ...
0.09791758, 0.24107521, 0.31352153, 0.31425553, 0.27684291, ...
0.18990934, 0.14168773, 0.10859684, 0.1049892 , 0.09133319, ...
0.0688494 , 0.06641062, 0.05996119, 0.04833707, 0.04299529, ...
0.04031001, 0.0391111 , 0.04241879, 0.03477004, 0.03336525, ...
0.02650127, 0.02101617, 0.01656881];
frequency = [0.0293 , 0.03906, 0.04883, 0.05859, 0.06836, 0.07813, 0.08789, ...
0.09766, 0.10742, 0.11719, 0.12695, 0.13672, 0.14648, 0.15625, ...
0.16602, 0.17578, 0.18555, 0.19531, 0.20508, 0.21484, 0.22461, ...
0.23438, 0.24414, 0.25391, 0.26367, 0.27344, 0.2832 , 0.29297, ...
0.30273, 0.3125 , 0.32227, 0.33203, 0.35156, 0.38086, 0.41016, ...
0.43945, 0.46875, 0.49805];
z = 0;
h = 22;
a1 = [0.012708, 0.009775, -0.079179, -0.074291, 0.201369, 0.2913 , ...
0.159335, 0.27175 , 0.236559, 0.301075, 0.30303 , 0.243402, ...
0.215054, 0.217986, 0.231672, 0.226784, 0.230694, 0.233627, ...
0.222874, 0.166178, 0.1652 , 0.192571, 0.184751, 0.115347, ...
0.13783 , 0.121212, 0.105572, 0.086022, 0.049853, 0.043988, ...
0.000978, -0.052786, -0.081134, -0.259042, -0.394917, -0.404692, ...
-0.478006, -0.502444];
b1 = [0.029326, -0.029325, -0.030303, 0.030303, 0.211144, 0.399805, ...
0.274682, 0.317693, 0.457478, 0.600196, 0.753666, 0.690127, ...
0.674487, 0.800587, 0.855327, 0.879765, 0.903226, 0.892473, ...
0.889541, 0.894428, 0.874878, 0.861193, 0.845552, 0.887586, ...
0.865103, 0.835777, 0.831867, 0.831867, 0.822092, 0.823069, ...
0.812317, 0.800587, 0.756598, 0.653959, 0.565005, 0.44868 , ...
0.397849, 0.370479];
[stokes_drift_east, stokes_drift_north] = stokes_drift(energy, frequency, z, h, a1, b1)
function [Stokes_spectral_east, Stokes_spectral_north] = stokes_drift(energy, frequency, z, h, a1, b1)
% Compute Spectral Stokes and Wave Bias Estimates (using Fourier moments)
depthflag = 'intermediate';
% Initialize with zero value prior to summing component-wise over freq
Stokes_spectral_east_0 = 0; % Surface value
Stokes_spectral_north_0 = 0; % Surface value
Stokes_spectral_east = zeros(size(z)); % At mean z of Signature bins
Stokes_spectral_north = zeros(size(z)); % At mean z of Signature bins
WaveBias_spectral_east_0 = 0; % Surface value
WaveBias_spectral_north_0 = 0; % Surface value
WaveBias_spectral_east = zeros(size(z)); % At mean z of Signature bins
WaveBias_spectral_north = zeros(size(z)); % At mean z of Signature bins
% Frequency resolution (*assumes constant*)
df = mean(abs(diff(frequency)));
% Loop over frequency
for jj=1:length(frequency)
om = 2*pi.*frequency(jj);
% Compute Stokes drift and Wave Bias for this frequency
if strcmp(depthflag,'intermediate')==1
k = wavenumber(frequency(jj), h);
Stokes_jj_0 = om*k*cosh(2*k*h)./(sinh(k*h).^2)*energy(jj);
Stokes_jj = om*k*cosh(2*k*(z+h))./(sinh(k*h).^2)*energy(jj);
WaveBias_jj_0 = om*k*cosh(2*k*h)./(sinh(k*h).^2)*energy(jj);
WaveBias_jj = om*k*cosh(k*z+2*k*h)./(sinh(k*h).^2)*energy(jj);
else
Stokes_jj_0 = om*k*energy(jj);
Stokes_jj = om*k*energy(jj)*exp(2*k*z);
WaveBias_jj_0 = om*k*energy(jj);
WaveBias_jj = om*k*energy(jj)*exp(k*z);
end
% Sum component-wise with contributions from other frequencies ** added factors of 2 in Mar 2021
Stokes_spectral_east_0 = Stokes_spectral_east_0+ 2*Stokes_jj_0.*(-a1(jj))*df;
Stokes_spectral_north_0 = Stokes_spectral_north_0 + 2*Stokes_jj_0.*(-b1(jj))*df;
Stokes_spectral_east = Stokes_spectral_east + 2*Stokes_jj.*(-a1(jj))*df;
Stokes_spectral_north = Stokes_spectral_north + 2*Stokes_jj.*(-b1(jj))*df;
WaveBias_spectral_east = WaveBias_spectral_east + 2*WaveBias_jj.*(-a1(jj))*df;
WaveBias_spectral_north = WaveBias_spectral_north + 2*WaveBias_jj.*(-b1(jj))*df;
WaveBias_spectral_east_0 = WaveBias_spectral_east_0 + 2*WaveBias_jj_0.*(-a1(jj))*df;
WaveBias_spectral_north_0 = WaveBias_spectral_north_0 + 2*WaveBias_jj_0.*(-b1(jj))*df;
end
end