Barotropic instability of shear flows

Barotropic instability of shear flows

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Zhiwu Lin, Georgia Tech
Fine Hall 322

We consider barotropic instability of shear flows for incompressible fluids with Coriolis effects. For a class of shear flows, we develop an approach by using the Hamiltonian structures of the linearized equation and an instability index formula to find the sharp stability conditions. We studied the flow with Sinus profile in details and found the sharp stability boundary in the whole parameter space, which corrected previous results in the fluid literature. The addition of the Coriolis force brings some fundamental changes to the stability of shear flows. Moreover, we also study the bifurcation of nontrivial traveling wave solutions and the linear inviscid damping near the shear flows. This is joint work with Hao Zhu and Jincheng Yang.