Variationally and numerically coupled water-wave and surf zone hydrodynamics

To improve the cost-effectiveness of modelling of wave interactions, a “numerical wavetank” is presented whose distinctive novel feature is its ability to couple both deep-water potential-flow and shallow-water models to controllable, prespecified wavemaker motion and beach topography. The coupling is in part obtained via a variational principle approach that guarantees important conservation properties and numerical stability. The model presented is the first fully nonlinear model to couple deep-water (discretised as finite elements) and shallow-water equations (discretised as finite volumes). Resulting simulations of wave generation, propagation and absorption by shallow-water-wave breaking are presented and analysed. A discussion is given on the efficacy of the novel approach.