This article is cited in 1 paper

On the propagation of long-wave perturbations in a two-layer free-boundary rotational fluid

A. A. Chesnokov

Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090

Abstract: A mathematical model for the propagation of long-wave perturbations in a free-boundary shear flow of an ideal stratified two-layer fluid is considered. The characteristic equation defining the velocity of perturbation propagation in the fluid is obtained and studied. The necessary hyperbolicity conditions for the equations of motion are formulated for flows with a monotonic velocity profile over depth, and the characteristic form of the system is calculated. It is shown that the problem of deriving the sufficient hyperbolicity conditions is equivalent to solving a system of singular integral equations. The limiting cases of weak and strong stratification are studied. For these models, the necessary and sufficient hyperbolicity conditions are formulated, and the equations of motion are reduced to the Riemann integral invariants conserved along the characteristics.

Keywords: two-layer fluid, shear flows, long waves, hyperbolicity.

UDC: 532.591+517.948

Received: 27.10.2003

 English version: Journal of Applied Mechanics and Technical Physics, 2004, 45:2, 230–238

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