INSTABILITY OF TWO UNIFORMLY STRETCHING PLANE LAYERS OF IDEAL FLUIDS
V.K. Andreev
Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk, Russia
Keywords: ideal fluid, free boundary, unsteady motion, stability
Abstract
The evolution of small perturbations in the joint motion of two uniformly stretched layers of ideal incompressible fluids is investigated. Kinematic and dynamic conditions are satisfied at the free boundaries of the layers and at their interface. The problem of small perturbations in Lagrangian coordinates is shown to admit separation of variables. A system of amplitude equations is derived that contains three Weber numbers, the density ratio and initial thickness ratio of the layers, and the wave numbers, making it possible to determine the evolution of the perturbed motion. Numerical results from an analysis of the amplitude equations are presented, indicating the instability of the motion under consideration.
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