Breaking criterion and characteristics for solitary waves on slopes

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Shoaling and breaking of solitary waves is computed on slopes from 1:100 to 1:8 using an experimentally validated fully nonlinear wave model based on potential flow equations. Characteristics of waves are computed at and beyond the breaking point, and geometric self-similarities of breakers are discussed as a function of wave height and bottom slope. No wave breaks for slopes steeper than 12°. A breaking criterion is derived for milder slopes, based on values of a nondimensional slope parameter So. This criterion predicts both whether waves will break or not and which type of breaking will occur (spilling, plunging, or surging). Empirical expressions for the breaking index and for the depth and celerity at breaking are derived based on computations. All results agree well with laboratory experiments. The nonlinear shallow water equations fail to predict these results with sufficient accuracy at the breaking point. Prebreaking shoaling rates follow a more complex path than previously realized. Postbreaking behaviors exhibit a rapid (nondissipative) decay, also observed in experiments, associated with a transfer of potential energy into kinetic energy. Wave celerity decreases in this zone of rapid decay.

Publication Title

Journal of Waterway, Port, Coastal and Ocean Engineering