Direct simulation of surface roughness signature of internal wave with deterministic energy-conservative model

In this simulation-based study, we investigate the surface roughness signature induced by internal solitary waves in oceans. We present the first-ever effort to directly capture the surface roughness signature with a deterministic two-layer model to avoid the singularity encountered in the traditional wave-current interaction theory. By capturing over four million wave components, the simulation resolves the surface wave and internal wave dynamics simultaneously. The surface signature characterized by a rough region followed by a smooth region travelling with an internal wave is quantified by the local wave geometry variation and the wave energy change. The surface wave dynamics are analysed in the wavenumber-frequency slope spectrum calculated in the frame moving with the internal wave. The asymmetric behaviours of right-moving and left-moving surface waves are found to contribute to the surface signature formation. Our results show that the formation of the surface signature is essentially an energy-conservative process and justify the use of the wave-phase-resolved two-layer model.