Spatio-temporal evolution of the surface wind-wave spectrum due to nonlinear internal solitary waves*

Internal solitary waves (ISW) in the ocean produce surface currents that modify surface waves in the capillary-gravity wave regime, leaving a distinct signature on the ocean surface of alternating rough and smooth banded patterns that are observable in synthetic aperture radar satellite imagery.  We study the evolution of the surface wave spectrum due to ISWs using a coupled surface-internal wave numerical model.  The surface waves are computed with a higher-order spectral method which solves for the velocity potential and free-surface elevation at the surface boundary. This model takes as its input the surface currents due to a propagating ISW computed with the Dubreil-Jacotin-Long (DJL) equation which gives the density and velocity field associated with fully nonlinear inviscid internal gravity waves. The surface waves are initialized with the JONSWAP spectrum, and we use the coupled model to simulate the surface wave spectrum in response to an ISW using parameters that are typical of those found in the South China Sea. The model is validated by comparison to results of the two-layer model of Hao and Shen (JFM 2020), and we present a detailed analysis of the spatio-temporal evolution of the surface wave spectrum due to the ISW.