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Three-dimensional stability of elliptical vortex columns in external strain flows. (English) Zbl 0872.76041

The authors consider various aspects of the dynamics of vortex patches of uniform vorticity embedded in flows of inviscid incompressible fluid with steady uniform strain and vorticity. The stability of these motions with respect to short-wave three-dimensional perturbations is studied by an application of geometrical optics stability technique. In the case of zero strain in the external flow, the stability problem is equivalent to the stability of steady elliptical flow in rotating frame. The stability equations have periodic coefficients and are analysed via Floquet technique. The main conclusion is that most such vortex flows are unstable. When the external flow has non-zero strain, the vortex patch typically pulsates periodically or elongates irreversibly. These flows are investigated by long-time simulations of governing equations. It was found that most of time-periodic flows are unstable, with growth rates that depend strongly on the parameters of the flow.

MSC:

76E99 Hydrodynamic stability
76B47 Vortex flows for incompressible inviscid fluids
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