Resonance Effects on Shoaling Surface Gravity Waves

📖 The Scoop

Two nonlinear shoaling models describing the shoaling of unidirectional surface gravity waves are developed. The models, based on variants of the Boussinesq equations for a sloping bottom are cast as a set of coupled evolution equations for the amplitudes and phases of the Fourier modes of the wave field. Resonant and near resonant triad interactions across the entire wind-wave frequency band (0.05-0.25 Hz) provide the mechanism for nonlinear cross spectral energy transfers and phase modifications as the waves propogate shoreward through the shoaling region (10 m - 3 m depth). A major field experiment designed to test the operational validity of the models was undertaken in the summer of 1980. Three representative data sets illustrating different initial spectral shape and subsequent evolution are compared in detail to predictions of the shoaling models and linear, finite-depth theory. The nonlinear shoaling models accurately predict Fourier coefficients of the wave field through the shoaling region for all data sets. Differences between the model predictions can be related to differences in the linear dispersion relations of the models. Measurements of directional spectra at two depths are used to partially explain coherence spectra between models and data.

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