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A Comparison of Two Formulations of Barotropic-Baroclinic Splitting for Layered Models
Robert L. Higdon
Oregon State University
(Abstract received 07/13/2007 for session X)
ABSTRACT
In the formulation of a barotropic-baroclinic splitting, the dependent variables in the layers can either be baroclinic quantities (u\',dp\') or the original unsplit variables (u,dp). In the second case, the variables in each layer are adjusted at each time step to ensure compatibility with the results produced from the barotropic equations. The second approach can be applied to the layer thickness equation to ensure exact conservation of mass within each layer. In the case of the momentum equations, the second approach amounts to replacing unresolved fast portions of Coriolis and pressure forcing with time averages of well-resolved forcing from the barotropic system. In this study, both approaches for the momentum equations are evaluated, in several test problems, by comparing to analytical solutions or to solutions computed with an unsplit code that uses short time steps. In several cases the two methods give very similar results. However, in some cases the second approach (u,dp) produces substantial grid noise. This noise can be suppressed with a sufficient amount of viscosity, but in one case the required viscosity produces major distortions in the flow field. In contrast, the first approach (u\',dp\') can be used with zero explicit viscosity and does not produce grid noise in these examples. All of these computations employ a two-level timestepping method that was previously developed by the author.
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2007 LOM Workshop, Bergen, Norway, August 20-22, 2007