SHOALING OF NONLINEAR INTERNAL WAVES ON A UNIFORMLY SLOPING BEACH

Kei Yamashita, Taro Kakinuma, Keisuke Nakayama

Abstract


The internal waves in the two-layer systems have been numerically simulated by solving the set of nonlinear equations in consideration of both strong nonlinearity and strong dispersion of waves. After the comparison between the numerical results and the BO solitons, as well as the experimental data, the internal waves propagating over the uniformly sloping beach are simulated including the cases of the mild and long slopes. The internal waves show remarkable shoaling after the interface touches the critical level. In the lower layer, the horizontal velocity becomes larger than the local linear celerity of internal waves in shallow water just before the crest peak and the position is defined as the wave-breaking point when the ratio of nonlinear parameter to beach slope is large. The ratio of initial wave height to wave-breaking depth becomes larger as the slope is milder and the wave nonlinearity is stronger. The wave height does not increase so much before wave-breaking on the mildest slope.

Keywords


nonlinear internal wave; two-layer system; variational principle; shoaling; wave-breaking point

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