A high accuracy/resolution spectral element method for the simulation of shoaling non-linear internal waves of depression over realistic bathymetry

The shoaling of an Internal Solitary Wave (ISW) of depression over the continental shelf can lead to a convective breaking of the wave along with the formation of a recirculating core, which has important implications for dissipation and mixing of the water column. The generation of this core is critically dependent on the near-surface vorticity structure of the background current. Such background currents can be driven by the internal tide but also by mesoscale/submesoscale eddies. This presentation will illustrate the fundamental components of a spectral-element-based incompressible flow solver explicitly designed to study shoaling ISWs and the associated turbulence in long, variable-bathymetry domains. Through a domain decomposition approach, the highly elongated computational domain can be broken down into a hierarchy of smaller problems which can be leveraged to achieve a robust solution of the incompressible Navier-Stokes equations. The efficacy of the numerical approach will be demonstrated via a suite of benchmarks. Additionally, the use and the implementation of a traction/free-slip boundary condition (BC) on the deformed boundary i.e. the actual bathymetry, will be discussed. More specifically, a free-slip BC can greatly alleviate the computational cost by avoiding the resolution of fine scale no-slip driven bottom boundary layers, thereby focusing on the efficient capture of the physics of interest in the ISW interior. As such, computational resources can be mainly allocated on the core of the wave allowing a more precise quantification of its breaking process. The presentation will conclude with preliminary results from a 3-D simulation of a shoaling ISW in the South China Sea.