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A Simple Wave Breaking Model with Quasi-Bore Model in Time Domain

Publication year Port and Airport Research Institute Report 042-02-02 2003.06
Author(s) Katsuya HIRAYAMA,Nobuhiko HARA
Department
/Divison
Marine Environment and Engineering Department Senior Research Engineer
Executive Summary

The Boussinesq model is widely employed to estimate non-linear wave transformation in shallow water. Reproduction of wave breaking phenomenon is done in the Boussinesq equation model with some approximation because the model obeys kinematics-boundary conditions for the continuous water surface. On the other hand, the wave and current deformation in the vicinity of the wave break point is more important in practical usage than wave breaking mechanism at a local point.
 In this study, the wave breaking model that doesn't depend on a bottom slope and the wave direction, and judges the occurrence of wave breaking more simply is suggested. The wave energy loss due to wave breaking is estimated with high accuracy in the new model. This model employs the judging function that vertical water pressure gradient decreases at wave breaking point. The energy loss due to wave breaking is estimated in a bore model that may reproduce the pressure head variation in an open channel. To apply the bore model to the wave transformation model in the Boussinesq equation which reproduces times-dependent water surface variation, we assume that the energy loss due to hydraulic jump bore in the small space and at a short time becomes the same to the wave energy loss in breaking during on unit of time.
 The simulation results are validated in the breaking wave experiment in a long wave tank. The newly developed wave breaking model is applicable to evaluate energy loss in the Boussinesq equation. The estimated distribution of breaking wave height in irregular wave propagation agreed well with that of wave height by Goda's model.
 This model, however, can not reproduce the wave breaking on offshore and on a gentle slope due to under estimating the breaker index. The improved wave breaking model is added another breaker index proposed by Yamada and Shiotani (1968). Consequently, distribution of wave height after breaking on a gentle slope agreed well with that of wave height calculated by the gradational breaking model proposed by Goda (2002). The wave energy loss due to wave breaking on the bar-type beach was not estimated with the improved model acquire sufncient accuracy.

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