Physical vs numerical dispersion in nonhydrostatic internal wave modeling
Most flows in the ocean are hydrostatic and so hydrostatic models are satisfactory for most applications of interest. However, when the
vertical scales are on the same order as the horizontal scales, such as in weakly nonlinear internal gravity waves, solution of the nonhydrostatic pressure may be required. Because solution of the nonhydrostatic pressure can incur substantial computational overhead, it is important to understand minimum grid resolution requirements that are sufficient to resolve the
nonhydrostatic internal waves while incurring as little computational overhead as possible. 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, errors in computing the hydrostatic pressure gradient can lead to erroneous numerical dispersion that mimics the effect of the nonhydrostatic pressure.
We show that in order for this numerical dispersion to be smaller than the physical nonhydrostatic dispersion, the grid resolution, Dx, must satisfy Dx/h
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Bio:
Oliver Fringer is assistant 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
study problems related to salt and sediment transport in estuaries, internal waves and mixing, and turbulence in rivers. Dr. Fringer received the US Office of Naval Research Young Investigator award in 2008 and was awarded
the US Presidential Early Career Award for Scientists and Engineers in 2009.