| Abstract: |
| The classical Rayleigh`s criterion gives a necessary condition for the linear instability of a zonal flow on a sphere. In this talk, we will see that it is far from sufficient for the 3-jet flow, and will give the sharp criteria. Mechanisms that induce unstable eigenvalues are provided. Furthermore, we will discuss nonlinear dynamics near the $3$-jet flow, as well as near some general steady flows. |
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