Ocean models typically employ the hydrostatic assumption because, for most problems of interest, vertical inertia is orders of magnitude smaller than horizontal inertia, thereby validating the assumption that vertical pressure variability arises purely from hydrostatics. This ultimately implies that horizontal scales of motion are much larger than vertical scales, and hence that the hydrostatic approximation is valid to simulate processes with large horizontal scales relative to the depth. The primary advantage of the hydrostatic assumption is that it eliminates computation of the nonhydrostatic pressure which can increase the computation time of typical oceanic calculations by one order of magnitude. Although most processes of interest in the ocean are hydrostatic, internal gravity waves exist over a wide range of horizontal scales and hence internal gravity waves with relatively short wavelengths are nonhydrostatic.

The primary physical effect of the nonhydrostatic pressure in internal gravity waves is frequency dispersion which causes waves of different frequencies to travel at different speeds. However, numerical errors can lead to erroneous numerical dispersion that mimics the effect of the nonhydrostatic pressure. In order for this numerical dispersion to be smaller than the physical nonhydrostatic dispersion, the horizontal grid resolution must be smaller than the relevant vertical depth scale, which can be the depth of the mixed layer. This can impose a significant computational overhead in 3D numerical simulations of internal gravity waves in the coastal ocean. The cost associated with the horizontal grid resolution requirement can be alleviated by assuming that a bulk of the internal wave energy in the ocean propagates as low-mode internal gravity waves. These waves are well-represented through use of a reduced number of isopycnal layers which follow the density surfaces, as opposed to use of many fixed vertical coordinates. The result can be a reduction in computational cost by up to two orders of magnitude. However, while isopcynal-coordinate models are commonly used in the ocean modeling community, none are nonhydrostatic.

In this presentation I will discuss nonhydrostatic modeling of internal gravity waves with an emphasis on development of a nonhydrostatic, isopycnal-coordinate ocean model to accurately and efficiently simulate nonhydrostatic internal gravity waves in the coastal ocean. I will discuss the model and associated approximations and present results of test cases to demonstrate model efficiency in comparison to standard z-level or fixed vertical-coordinate techniques.

Oliver Fringer is associate professor in the Department of Civil and Environmental Engineering at Stanford University, where he has been since 2003. He received his BSE from Princeton University in Aerospace Engineering and then received an MS in Aeronatics and Astronautics, followed by a PhD in Civil and Environmental Engineering, both from Stanford University. His research focuses on the application of numerical models and parallel computing to the study of laboratory- and field-scale environmental flows to understand the physics of salt and sediment transport in lakes and estuaries, internal waves and mixing, and turbulence in rivers. Dr. Fringer received the ONR Young Investigator award in 2008 and was awarded the Presidential Early Career Award for Scientists and Engineers in 2009.