A model to simulate nonhydrostatic internal gravity waves in the ocean

Abstract:

Internal gravity waves in the ocean are primarily generated due to tidal flow over topography that generates internal tides, or internal waves of tidal frequency. As they propagate, internal tides steepen into trains of internal solitary waves that eventually break upon interacting with shallow coastal topography. Modeling internal solitary waves is difficult because they have length scales that are short relative to the internal tide, and so many grid points in three dimensions are needed to accurately resolve their evolution. Because internal solitary waves arise from a balance between nonlinear advection of momentum and nonhydrostatic dispersion, they must be simulated with nonhydrostatic ocean models. Such models are expensive because computation of the nonhydrostatic pressure requires solution of a three-dimensional Poisson equation that can incur an order of magnitude increase in the computational cost. Finally, because internal solitary waves can propagate over long distances with little to no dissipation or mixing of the thermocline upon which they propagate, the numerical model must minimize spurious vertical numerical diffusion of the density field.

We will discuss development of a new ocean model designed to accurately simulate internal solitary waves. Horizontally unstructured, finite-volume grids are employed to enable resolution of the multiscale nature of internal solitary waves by refining the grid where they are likely to form. To resolve the nonlinear-nonhydrostatic balance in the waves, the model computes the nonhydrostatic pressure, but with a preconditioner that ensures minimal overhead where the nonhydrotatic pressure is not needed. Finally, to minimize spurious numerical diffusion, we employ an Arbitrary-Lagrangian-Eulerian (ALE), or hybrid, vertical coordinate system in which the vertical direction is discretized with boundary-following (sigma or s), Cartesian (z), or density-following (isopycnal) coordinates. Because isopycnal coordinates follow lines of constant density, they ensure no spurious vertical numerical diffusion of density. We will discuss numerical discretization issues and present test cases that highlight the unique features of the model.