This article is cited in 6 papers

Wave motion of an ideal fluid in a narrow open channel

A. A. Chesnokov^ab, V. Yu. Lyapidevskii<sup>ab

a</sup> Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090, Russia
^b Novosibirsk State University, Novosibirsk, 630090, Russia

Abstract: This paper considers a nonlinear integrodifferential model constructed for the motion of an ideal incompressible fluid in an open channel of variable section using the long-wave approximation. A characteristic equation for describing the perturbation propagation velocity in the fluid is derived. Necessary and sufficient conditions of generalized hyperbolicity for the equations of motion are formulated, and the characteristic form of the system is calculated. In the case of a channel of constant width, the model reduces to the Riemann integral invariants which are conserved along the characteristics. It is found that, during the evolution of the flow, the type of the equations of motion can change, which corresponds to long-wave instability for a certain velocity distribution along the channel width.

Keywords: long-wave approximation, horizontal shear flows, integrodifferential equations, hyperbolicity.

UDC: 532.591+517.948

Received: 05.11.2008

 English version: Journal of Applied Mechanics and Technical Physics, 2009, 50:2, 220–228

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