NONLINEAR EVOLUTION OF SURFACE-WAVE SPECTRA ON A BEACH

The shoaling evolution of wave spectra on a beach with straight and pa rallel depth contours is investigated with a stochastic Boussinesq mod el. Existing deterministic Boussinesq models cast in the form of coupl ed evolution equations for the amplitudes and phases of discrete Fouri er modes describe accurately the shoaling process for arbitrary incide nt wave conditions, but are numerically cumbersome for predicting the evolution of continuous spectra of natural wind-generated waves. The s tochastic formulation used here, based on the closure hypothesis that phase coupling between quartets of wave components is weak, predicts t he shoaling evolution of the continuous frequency spectrum and bispect rum of the wave field. The general characteristics of the stochastic m odel and the dependence of wave shoaling on nonlinearity, initial spec tral shape, and bottom profile are illustrated with numerical simulati ons. Predictions of stochastic and deterministic Boussinesq models are compared with data from a natural barred ocean beach. Both models acc urately reproduce the observed nonlinear wave transformation for a ran ge of conditions.