A theoretical model is developed for wave heights and setup in a surf zone. In the time averaged equations of energy and momentvmi the energy flux, radiation stress and energy dissipation are determined by simple approximations which include the surface roller in the breaker. Comparison with measurements shows good agreement. Also the transitions immediately after breaking are analysed and shown to be in accordance with the above mentioned xdeas and results.

Shoaling and breaking of solitary waves is computed on slopes 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 S o. 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 NSW equations fail to predict these results with sufficient accuracy at the breaking point. Pre-breaking shoaling rates follow a more complex path than previously realized. Post-breaking behaviors exhibit a rapid (non-dissipative) decay, also observed in experiments, associated with a transfer of potential energy into kinetic energy. Wave celerity decreases in this zone of rapid decay.

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Measurements of turbulent kinetic energy k under surf zone waves are analyzed to show how k varies over depth, between breaker point and shoreline, and how k depends on the beach slope. It is found that the variation of k over depth is remarkably weak, large values being measured a few percent of the depth above the bottom. A simple model for the dissipation mechanism makes it possible to derive an empirical formula for the timeaveraged k that accurately describes all the data considered reliable. Denmark, 1979. Hansen, J. B., and I. A. Svendsen, A theoretical and experimental study of undertow, Proc. Int.