New PDE reduced models for rotating stratified flows

Monday, February 22, 2010 - 2:00pm - 2:45pm
EE/CS 3-180
Leslie Smith (University of Wisconsin, Madison)
Keywords: Boussinesq equations, wave-vortical interactions, quasi-geostrophic approximation,
intermediate models

Abstract: Starting from the rotating Boussinesq equations, we show
how to derive a hierarchy of new models intermediate
between the quasi-geostrophic (QG) approximation and
the full equations. The new PDEs progressively include
more effects of inertia-gravity waves. We explain how to
derive the new models in two ways: (i) by eigenmode projection,
and (ii) directly in physical space. We illustrate how the
new reduced PDEs can be used to identify the nonlinear interactions primarily responsible for observed non-QG phenomena, such as
cyclone/anticyclone asymmetry in geophysical flows.
A waves-only model gives insight into the growth of
horizontal shear flows. Simulations of the models highlight
the practical implications of under-resolving wave-mode
interactions in numerical calculations.
MSC Code: