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Stochastic nonlinear shoaling of directional spectra

Published online by Cambridge University Press:  25 August 1997

Y. AGNON
Affiliation:
Present address: Centre for Computational Hydrodynamics (ICCH), Danish Hydraulic Institute, Agern Alle 5, DK-2970 Hørsholm, Denmark. Department of Civil Engineering, Technion, Haifa 32000, Israel
A. SHEREMET
Affiliation:
CAMERI – Coastal and Marine Engineering Research Institute, Technion City, Haifa 32000, Israel

Abstract

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.

Type
Research Article
Copyright
© 1997 Cambridge University Press

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