Numerical study of surface-internal wave interaction based on a two-layer fluid model

The interaction between surface waves and internal waves is an important physical process in oceans. It is challenging to simultaneously resolve the surface waves and internal waves from the first principles of hydrodynamics because of the large difference in their length scales. In this study, we conduct numerical simulations based on a two-layer fluid model with the assumption of potential flow, and the dynamics of surface waves and internal waves are captured in phase-resolved simulation. The initial condition is a linear superposition of the eigenfunctions of the model, including the surface wave modes adapted from the JONSWAP spectrum and the internal wave modes reconstructed from the solutions of a KdV-type equation. In our results, we observe a distinct roughness change in the surface wave field, with a smooth region adjacent to a rough region. We have quantified this roughness change using the local steepness and wavenumber spectrum. Further analysis in the wavenumber-frequency space shows that short surface waves are reflected by the internal wave-induced motion. Our result suggests that the internal wave-induced motion plays a key role in the formation of surface signatures.