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Center for Nonlinear Studies |
The Boussinesq equations are an approximation to the rotating compressible Navier-Stokes equations that accurately model many geophysical flows. They are still difficult to deal with analytically, so a variety of methods are used to simplify them in order to glean insight into their behaviour. In this talk, we look at what happens when rotation is much more important than advection or stratification. We analyze the equations using both a standard asymptotic expansion and a multiple-time scale asymptotic expansion. Even though the standard expansion filters out gravity waves, while the multiscale method allows fast-moving gravity waves of any amplitude, the two approaches give almost identical results for the slow-moving parts of the flow. This is also true for other asymptotic scalings that are relevant to atmospheric and oceanic flows. We discuss why this is so, and how the existence of a particular kind of conservation law, such as the conservation of potential vorticity, can be used to show this.
Host: Todd Ringler