Tradeoffs between complexity and accuracy in nonhydrostatic ocean modeling
Oliver Fringer, Department of Civil and Environmental Engineering, Stanford University
4 – 5PM
Thursday May 17, 2012
POB 2.302 (AVAYA)
Abstract
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