STOCHASTIC NONLINEAR SHOALING OF DIRECTIONAL SPECTRA

We derive a deterministic directional shoaling model and a stochastic directional shoaling model for a gravity surface wave field, valid for a beach with parallel depth contours accounting for refraction and no nlinear quadratic (three wave) interactions. A new phenomenon of non-r esonant spectral evolution arises due to the medium inhomogeneity. The kernels of the kinetic equation depend on the bathymetry through an i ntegral operator. Preliminary tests carried out on laboratory data for a unidirectional case indicate that the stochastic model also works r ather well beyond the region where the waves may be regarded as nearly Gaussian. The limit of its applicability is decided by the dispersivi ty of the medium (relative to the nonlinearity). Good agreement with b oth laboratory data and the underlying deterministic model is found up to a value of about 1.5 for the spectral peak Ursell number. Beyond t hat only the deterministic model matches the measurements.