Dispersion relations and phase velocities of surface gravity waves, with their non-linearity being considered, have been derived numerically from an equation for a nonvortical incompressible fluid of finite depth. For all the depths being considered, the dispersion relations are readily realized for the wavenumbers smaller than the wavenumber of the basic harmonic. Then the acquired relations tend to increasingly deviate from the linear dispersion relations. This is the case for all the depths and wave steepnesses under discussion. When the depth of the sea diminishes, the deviations dramatically increase in both cases, when waves grow steeper and when the form of the wave spectrum changes from wide to narrow. This also holds for the phase velocity of waves.
Physical Oceanography – Springer Journals
Published: Oct 28, 2006
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