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Instability criteria for steady flows of a perfect fluid. (English) Zbl 1055.76518
Summary: An instability criterion based on the positivity of a Lyapunov-type exponent is used to study the stability of the Euler equations governing the motion of an inviscid incompressible fluid. It is proved that any flow with exponential stretching of the fluid particles is unstable. In the case of an arbitrary axisymmetric steady integrable flow, a sufficient condition for instability is exhibited in terms of the curvature and the geodesic torsion of a stream line and the helicity of the flow.

MSC:
76E99 Hydrodynamic stability
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
76B99 Incompressible inviscid fluids
76E30 Nonlinear effects in hydrodynamic stability
76F20 Dynamical systems approach to turbulence
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