Nonlinear model predictions of bispectra of shoaling surface gravity waves

Boussinesq-type nonlinear equations for waves propagating over a sloping bottom are shown to accurately model the evolving bispectra of a spectrum of non-breaking shoaling ocean-surface gravity waves. The model response to a variation of the gentle, constant beach slope and the amount of nonlinear (i.e. non-random) phase coupling in the initial conditions is also examined. Variation of these quantities results in relatively little change in the overall structural evolution of the bicoherence and biphase (related to the nonlinear modification of the wave shape). The apparent unimportance of bottom slope motivates consideration of constant-depth KdV equations. Simple analytic solutions are found for harmonic growth in the special case of a monochromatic primary wavetrain. The associated bispectral evolution is qualitatively similar to field observations and to predictions based on the full Boussinesq model for a sloping bottom.