Large Eddy Simulation of Internal Breaking Waves

Oliver Fringer, Stanford University

The ocean is a stratified medium. As a result, waves can propagate horizontally at density interfaces or at an angle to the horizontal within continuously stratified regions. A significant portion of internal wave energy along coastal regions is generated by the interaction of the surface tides with the bottom topography. The surface, or barotropic, tide perturbs the density profile as different density fluids are forced over topography at the edges of the continental shelves. These perturbations generate internal waves at tidal frequency, or internal tides, that propagate both out to the open ocean as well as on to the continental shelf. Under the right conditions, internal waves can focus enough energy at a point such that either a shear or convective instability can form and cause them to break. This breaking process generates turbulence and mixing that can cause significant sediment transport and nutrient redistribution and can modify acoustic wave propagation and optical clarity within the littoral ocean. Furthermore, breaking internal waves are thought to account for a significant portion of the dissipation within the ocean, concentrating most of it at coastal boundaries. This project focuses on a large eddy simulation of the internal wave breaking process at an interface between two fluids of different densities. In order to create internal breaking waves, the instability can be forced by either the use of characteristic focusing or by wave steepening due to topographic effects. Characteristic focusing relies on the dispersive nature of internal waves. By sending out short, slow waves followed by long, fast waves, an internal wave chirp signal can be generated in which the fast waves overtake the slow waves and focus to a point at which they generate a breaking instability. On the other hand, sending an internal wave train over sloped topography causes unstable growth in wave amplitude that leads to a breaking instability as well.

The present numerical study is performed in conjunction with a laboratory scale study in order to verify the results. With these results, the goal is to parameterize the dissipative mechanisms of internal wave breaking in order to allow a full-scale simulation of internal wave breaking in Monterey Bay on a Beowulf cluster of Pentium III workstations. The model we use incorporates a free surface as well as a nonhydrostatic pressure solver. Typically, numerical simulations of coastal processes do not solve for the nonhydrostatic pressure as the hydrostatic approximation holds for most cases. In Monterey Bay, however, measurements have shown that the internal-wave energy cascade transfers enough energy to the nonhydrostatic regime to make a nonhydrostatic model a necessity. This increases the required resolution to roughly 8 million grid points for a reasonable simulation of Monterey Bay, making parallel computation a necessity as well.

Abstract Author(s): Oliver Fringer