A Directional Decomposition Method to Estimate the Reflection and Transmission of Nonlinear Internal Waves Over a Slope

Multi-directional propagating nonlinear internal waves (NLIWs) create complex spatial patterns, often making it difficult to quantitatively estimate the reflection and dissipation processes of NLIW energy over a slope. To identify the onshore- and offshore-going wave signals in a regional model, we apply a directional Fourier filter (DFF) method to clarify wave dynamics over varying slopes. First, a series of two-dimensional analytical solutions of either solitons or NLIW packets are utilized. Next, two-dimensional numerical experiments indicate that the rate of reflection (dissipation) of energy for the shoaling NLIWs is much lower (higher) than that for the shoaling internal tides over a slope, regardless of varying slope criticality and height. Finally, we apply the DFF method in a three-dimensional non-hydrostatic regional model (MITgcm) to directionally decompose the onshore- and offshore-going internal waves (IWs) on the Australian North West Shelf. The model results show that mode-1 incoming internal tides gradually steepen into NLIWs during the shoaling processes over the slope, and then the reflecting IWs are propagate offshore in the main form of linear IW beams. In addition, the reflectivity of IWs around the Imperieuse Reef is 60% and the offshore-reflecting IWs quickly dissipate accompanied by an e-folding length scale of similar to 22 km.

Automated summary

This study investigates the reflection and dissipation processes of nonlinear internal waves (NLIWs) over a slope. They find that the rate of reflection of NLIWs is lower than that of internal tides, and that incoming internal tides gradually transform into NLIWs during the shoaling process. The study also shows that around Imperieuse Reef, 60% of the offshore-reflecting internal waves dissipate with an e-folding length scale of about 22 km.