Instability criteria for steady flows of a perfect fluid.
Instability criteria for steady flows of a perfect fluid.
复制标题
完美流体稳定流动的不稳定性标准。
作者：
S. Friedlander;M. Vishik
基于 Lyapunov 型指数正性的不稳定准则用于研究控制无粘不可压缩流体运动的欧拉方程的稳定性。证明任何具有流体粒子指数拉伸的流动都是不稳定的。在任意轴对称稳态可积流的情况下，流线的曲率和测地线扭力以及流动的螺旋度表现出不稳定的充分条件。
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.