"The onset of instability for zonal stratospheric flow"Zhiwu LinWe investigate some qualitative aspects of the dynamics of the Euler equation on a rotating sphere that are relevant for 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, which corresponds to choosing the Legendre polynomial of degree n as the stream function. Since the 1-jet and the 2-jet are stable, the main interest is the onset of instability for the 3-jet. We confirm conjectures based on numerical simulations by proving that there exist positive and negative critical rotation rates for the linear instability of 3-jet. Turning to the nonlinear problem, we prove that linear instability implies nonlinear instability and that, as the rotating rate goes to infinity, nearby traveling waves gradually change from a cats’s eyes streamline pattern to a profile with no stagnation points. This is a joint work with Adrian Constantin, Pierre Germain and Hao Zhu. |
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