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Tradeoffs between complexity and accuracy in nonhydrostatic ocean modeling

Thursday, May 17, 4PM – 5PM
POB 2.302 (AVAYA)

Oliver Fringer

Ocean models make several approximations to the Navier-Stokes equations based on the temporal and spatial scales of motion that can be resolved by the computational grid. Due to limitations in computational power, it will be quite some time before ocean models can capture small-scale turbulent processes related to mixing and dissipation. However, computer performance is now enabling ocean models which havehistorically been hydrostatic to resolve processes in which the nonhydrostatic or elliptic component of the pressure field is important. In this talk I will discuss minimum grid resolution requirements that are sufficient to resolve nonhydrostatic processes in the ocean with a focus on internal gravity waves. Internal gravity waves are unique from a computational perspective because they possess horizontal length scales that span both hydrostatic and nonhydrostatic regimes.

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. I will show that in order for this numerical dispersion to be smaller than the physical nonhydrostatic dispersion, the grid resolution, dx, must satisfy dx/h<O(1), where h is the relevant depth scale. This constraint shows that predictions of nonhydrostatic internal gravity waves in coastal domains with three-dimensional nonhydrostatic models require simulations with 100s of millions of grid cells. Solution of elliptic problems of this size are challenging even on today's fastest supercomputers. Therefore, I will discuss the advantages of employing a much faster reduced-order model that, although it eliminates a host of physical processes, the model captures the dominant two-dimensional nonhydrostatic physics more accurately than its fully three-dimensional, nonhydrostatic counterpart.

Short bio: 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 Aeronautics 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 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.

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