The Onset of Instability for Zonal Stratospheric Flows
par
Amphithéâtre Léon Motchane
IHES
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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Zhongkai Tao & Jian Wang