Nonlinear Coupling in Waves Propagating Over a Bar

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Abstract
The degree of nonlinear coupling in a random wavefield propagating over and beyond a bar is examined using a physical wave flume as well as numerical simulations based on time-domain extended Boussinesq equations and their frequency-domain counter-part. The nonlinear phase speed is computed from the evolution of the nonlinear part of the phase function inherent in the frequency-domain model. Over the bar, the phase speeds of the higher harmonics are larger than the linear estimates due to the nonlinear couplings, resulting in virtually dispersionless propagation, while beyond the bar crest, nonlinear effects on the phase speed vanish rapidly, implying full release of bound harmonics. Quantitative measures of nonlinearity such as the skewness and asymmetry have also been determined. They have near-zero values in the deep-water region on either side of the bar and a pronounced peak over the bar. On the downwave side, the random wave field is found to be spatially homogeneous. This implies that it can be fully described by the energy density spectrum without additional phase information related to the bar location.