Direct Simulation of the Surface Manifestation of Internal Gravity Waves with a Wave–Current Interaction Model

Internal solitary waves in the ocean are characterized by the surface roughness signature of smooth and rough bands that are observable in synthetic aperture radar satellite imagery, which is caused by the interaction between surface gravity waves and internal wave–induced surface currents. In this work, we study the surface signature of an internal wave packet in deep water over a large range of spatial scales using an improved wave–current interaction model that supports a moving surface current corresponding to a propagating internal gravity wave. After validating the model by comparison to previously published numerical results by Hao and Shen, we investigate a realistic case based on a recent comprehensive field campaign conducted by Lenain and Pizzo. Distinct surface manifestation caused by internal waves can be directly observed from the surface waves and the associated surface wave steepness. Consis-tent with observations, the surface is relatively rough where the internal wave–induced surface current is convergent (­U/­x, 0), while it is relatively smooth where the surface current is divergent (­U/­x. 0). The spatial modulation of the surface wave spectrum is rapid as a function of along-propagation distance, showing a remarkable redistribution of energy under the influence of the propagating internal wave packet. The directional wavenumber spectra computed in the smooth and rough regions show that the directional properties of the surface wave spectra are also rapidly modu-lated through strong wave–current interactions. Good agreement is found between the model results and the field ob-servations, demonstrating the robustness of the present model in studying the impact of internal waves on surface gravity waves.