The Onset of Instability for Zonal Stratospheric Flows

Séminaire d’Analyse
In this talk, we discuss some qualitative aspects of the dynamics of the Euler equation on a rotating sphere that are relevant or stratospheric flows. Zonal flow dominates the dynamics of the stratosphere and for most known planetary stratospheres the observed flow pattern is a small perturbation of an n-jet. Since the 1-jet and the 2-jet are stable, the main interest is the onset of instability for the 3-jet. We prove that the 3-jet is linearly unstable if and only if the rotation rate belongs to a critical interval. Turning to the nonlinear problem, we prove that linear instability implies nonlinear instability and that, as the rotation rate goes to infinity, nearby traveling waves change gradually from a cat’s eyes streamline pattern to a profile with no stagnation points. This talk is based on a joint work with Profs. Adrian Constantin, Pierre Germain and Zhiwu Lin.
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