Influence Mechanism of Continental Slope on the 2D Propagation and Evolution of Internal Solitary Waves

Internal solitary waves (ISWs) are widely distributed in marginal sea areas. When propagating over steep and complex continental slopes and shelves, ISWs will undergo deformation and breaking, thereby enhancing vertical mixing and energy transfer in the inner ocean and playing an important role in Earth’s biogeochemical cycles. In marginal seas, basin-scale topography not only influences the along-propagation direction evolution of ISWs, but also affects their transverse diffraction, leading to asymmetric structures along the basin axis observed in satellite imagery.

In this work, a theoretical model based on the variable-coefficient Kadomtsev-Petviashvili (vKP) equation is developed to reveal the influence of continental slopes within basin topography on the transverse diffraction of ISWs, and to explain the mechanisms governing the 2+1-dimensional propagation and evolution of ISWs over the slopes of the Sulu Sea. Using the climatological annual-mean density and bathymetry of the Sulu Sea, two idealized configurations are constructed in which topographic variations are isolated to either the along-propagation direction or the cross-propagation direction. The results show that all the dynamical coefficients vary most significantly over the slope region with water depths between 300-3000 m.

Numerical simulations of the vKP model indicate that cross-propagation direction slope variations play a dominant role in shaping the two-dimensional spatial distribution of ISWs. The asymmetric distribution of ISWs along the basin axis is primarily caused by phase speed differences induced by depth variations. In contrast, both the along- and cross-propagation directions slope variations influence the waveform evolution of ISWs. Enhanced nonlinearity in shallower regions leads to waveform steepening and larger amplitudes, whereas weaker nonlinearity and reduced amplitudes are found on the deeper side.

Furthermore, based on the simulation results, the spatial distributions of ISW energy and energy flux in the Sulu Sea are estimated. Although ISWs on the deeper side exhibit smaller amplitudes, their energy flux is significantly stronger, reaching approximately 10 kW/m, which is twice the flux on the shallow side.