Journal of Fluid Mechanics

Research Article

Stochastic nonlinear shoaling of directional spectra

Y. AGNON a1 and A. SHEREMET a2
a1 Department of Civil Engineering, Technion, Haifa 32000, Israel
a2 CAMERI – Coastal and Marine Engineering Research Institute, Technion City, Haifa 32000, Israel


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 nonlinear quadratic (three wave) interactions. A new phenomenon of non-resonant spectral evolution arises due to the medium inhomogeneity. The kernels of the kinetic equation depend on the bathymetry through an integral operator. Preliminary tests carried out on laboratory data for a unidirectional case indicate that the stochastic model also works rather well beyond the region where the waves may be regarded as nearly Gaussian. The limit of its applicability is decided by the dispersivity of the medium (relative to the nonlinearity). Good agreement with both laboratory data and the underlying deterministic model is found up to a value of about 1.5 for the spectral peak Ursell number. Beyond that only the deterministic model matches the measurements.

(Received May 17 1996)
(Revised March 19 1997)


Present address: Centre for Computational Hydrodynamics (ICCH), Danish Hydraulic Institute, Agern Alle 5, DK-2970 Hørsholm, Denmark.