Dissipation of nonlinear shallow water waves

Nonlinear frequency domain formulations of extended Boussinesq equations are studied. The new formulation retains the natural split between continuity and momentum equations, allowing for the dissipation term to be incorporated directly into the momentum equation. Additionally, due to the strong resemblance to the time domain equation, an inverse FFT technique can be used to calculate the nonlinear terms in the time domain, enacting a substantial computational savings. Lastly, a recently-published parameterization for the evolutionary behavior of the high wavenumber tail of surf zone spectra was tested against laboratory data. The experimental parameters of these data may be near the limits of validity for the parameterization, yet the formulation works surprisingly well. These encouraging results may lead the way toward incorporating the parameterization into a nonlinear wave transformation model.