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On the three-dimensional instability of strained vortices. (English) Zbl 0696.76052
Summary: The three-dimensional instability of a two-dimensional flow with elliptical streamlines has been proposed as a generic mechanism for the breakdown of many 2-D flows. A physical interpretation for the mechanism is presented together with an analytical treatment of the problem. It is shown that the stability of an elliptical flow is governed by an Ince equation. An analytical representation for a localizd solution is given and establishes a direct link with previous computations and experiments.

MSC:
76E05 Parallel shear flows in hydrodynamic stability
76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations
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[1] DOI: 10.1017/S0022112083000518 · Zbl 0556.76039 · doi:10.1017/S0022112083000518
[2] DOI: 10.1063/1.864226 · doi:10.1063/1.864226
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