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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. Yet, 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 will introduce the Boussinesq equations, discuss the parameters that are important to their behaviour, and show how aymptotic methods can be used to simplify the equations in parameter regimes of geophysical importance. We will then discuss the applications to turbulence, and how these methods may show the existence of new intertial ranges for energy and enstrophy in the different asymptotic limits, similar to those predicted by Kolmogorov's 4/5ths law.