Modelling of Wave Breaking in Boussinesq Evolution Equations

A new breaking formulation for deterministic evolution equations in the frequency domain is developed. In contrast to conventional breaking formulations based on a bulk energy dissipation model, the new model is based on the surface roller model, which is known to model breaking well in time domain Boussinesq formulations. The toggling between the frequency and time domain is performed using Fast Fourier Transform. Fast Fourier Transform is furthermore used for reducing the computational work in each spatial point from O(N²) to O(N log N), N being the number of frequency components. Initial results for the spilling breaker test of Ting and Kirby show that the new model is able to describe wave height decay satisfactorily. Due to the equivalence with the time domain breaking formulation, an improvement in wave shape was expected when comparing to traditional breaking models in the frequency domain. Surprisingly, this improvement is only marginal at present.