Transformation of Statistical Properties of Shallow-Water Waves
Directional shallow-water statistical properties of water waves are determined by linear transformation from their deep-water properties. Universal relationships between deep- and shallow-water joint probability distributions of wave height, wave period, and wave direction are established. The formulations are applied to the case of directional narrow-band spectra over a plane bathymetry in intermediate water depth. It is shown that the wave height statistical distributions no longer remain Rayleigh as in deep water, and the wave period distribution is no longer Gaussian but is skewed as a function of water depth. It can be concluded that when waves propagate in intermediate water depth from deeper regions to shallower, the skewness of the marginal probability contours shifts from longer waves to shorter waves.
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