goffAbyssalHillTopography

Generate periodic Goff abyssal-hill topography.

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Declaration

 [virtualDepth,topographicHeight,diagnostics] = WVPseudoTopographicWaveGeneration.goffAbyssalHillTopography(wvt,options)

Parameters

• wvt periodic WVTransform defining the horizontal grid and mean depth
• options.rmsHeight requested post-filter RMS topographic height in meters
• options.cornerWavenumber Goff corner wavenumber in radians per meter
• options.minimumWavelength shortest retained wavelength in meters
• options.randomSeed nonnegative seed for a local Mersenne Twister stream

Returns

• virtualDepth positive water depth of size \(N_x\times N_y\) in meters
• topographicHeight upward-positive zero-mean height of size \(N_x\times N_y\) in meters
• diagnostics realized statistics and spectral diagnostics

Discussion

The isotropic two-dimensional power spectrum is

\[P_h(K)=\frac{4\pi h_{\mathrm{rms}}^2}{K_c^2} \left(1+\frac{K^2}{K_c^2}\right)^{-2}.\]

The returned height is positive upward, zero mean, and normalized to the requested post-filter RMS. Random phases use a local stream and do not alter MATLAB’s global random state.

  [H,h,diagnostics] = WVPseudoTopographicWaveGeneration.goffAbyssalHillTopography(wvt,minimumWavelength=30e3);