A high-order spectral method for effective simulation of surface waves interacting with an internal wave of large amplitude

Abstract

In this study, we propose a new method for simulating complex surface waves interacting with a large amplitude internal solitary wave. Our model is based on a high-order spectral method for surface waves with the bottom boundary conditions computed from an internal wave solver. The convergence of the model is first tested using an internal wave case without surface waves. We then perform simulations of a canonical nonlinear wave interaction case involving two surface wave components and a prescribed internal wave component. The initial wave energy growth rate of the resonant wave component is found to agree with the analytical value predicted by the perturbation theory. We also use the model to simulate the interaction between surface waves and a weakly nonlinear internal wave, and the result is nearly identical to that calculated using a two-layer model. Finally, we show the application of our model in a multiscale nested modeling framework, where the internal wave parameters are extracted from the mesoscale simulation using a nonhydrostatic ocean model. The evolution of the spatial variations of the surface roughness is captured and the surface wave orbital velocity also changes in space due to the surface motions induced by the internal wave. Our phase-resolved model provides a computationally efficient tool for simulating complex surface wave fields in the background of internal waves of large amplitudes.