Wave breaking in Boussinesq models for undular bores

摘要

A nonlinear dispersive model equation is used to study the onset of breaking in long waves behind the front of an undular bore. According to experiments conducted by Favre (1935) [1], weak bores have a smooth, but oscillatory structure, with undulations appearing behind the bore front. With increasing bore strength, the amplitude of these oscillations grows until one or several of them start breaking. The change in type from the purely undular bore occurs at a sharply defined depth ratio which is under review in this article. A convective breaking criterion is put forward, and numerical computations are used to compare the predictions of this model to Favres wavetank experiments. It appears that the numerical results underpredict the appearance of breaking waves, but are in good qualitative agreement with the experiments. The results are interpreted with the aid of exact solitary-wave solutions, and it is found that the transition from purely undular to breaking bore may be recast with the help of a breaking criterion for solitary waves.