Processes in the ocean span a range of spatiotemporal scales. However, most numerical models are designed to simulate specific coastal processes or specific spatiotemporal scales. Furthermore, numerical models are subject to many sources of error arising from discrete approximations to continuous equations governing fluid motion (e.g. conservation of mass, momentum). Increases in computer power and grid resolution reduce numerical errors, improving and expanding the range of physical processes represented in the model. However, many important processes (e.g. turbulence) remain sub-grid scale.

In this talk, I discuss several challenges in ocean modeling and my research efforts overcome them. In particular, I focus on my dissertation work to develop a new ocean model (a nonhydrostatic, isopycnal-coordinate model) to improve simulations of internal waves, which represent a critical yet poorly-understood component of the ocean’s energy budget. The goal of this new model is to simulate internal waves using a reduced number of vertical layers without resorting to the hydrostatic approximation. Because many small-scale internal waves, such as internal solitary waves, are a balance between nonlinearity and nonhydrostatic dispersion, models invoking the hydrostatic approximation do not permit their formation (except through a balance of nonlinearity and numerically-induced dispersion).