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

Abstract

Abstract 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. Consistent 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 modulated through strong wave–current interactions. Good agreement is found between the model results and the field observations, demonstrating the robustness of the present model in studying the impact of internal waves on surface gravity waves. Significance Statement The purpose of this study is to better understand the physical processes leading to the bands of rough and smooth surface waves arising from internal gravity waves. The surface manifestation of internal gravity waves allows them to be measured remotely via surface imagery, which can provide insight into their nonlinear behavior and sources and fate and which can ultimately inform the local stratification for assimilation into larger-scale models. Our results highlight the application of wave–current interaction models to the study of the interaction of surface waves with internal gravity waves and indicate strong modulation of the surface wave spectra over relatively short time scales despite the long time scales associated with the internal wave propagation.