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Experimental study of interfacial long waves in a two-layer shear flow

Published online by Cambridge University Press:  26 April 2006

Pierre Barthelet ,
François Charru  and
Jean Fabre
Pierre Barthelet
Affiliation:
Institut de Mécanique des Fluides, 2, allée du Professeur C. Soula, 31400 Toulouse, France
François Charru
Affiliation:
Institut de Mécanique des Fluides, 2, allée du Professeur C. Soula, 31400 Toulouse, France
Jean Fabre
Affiliation:
Institut de Mécanique des Fluides, 2, allée du Professeur C. Soula, 31400 Toulouse, France
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Abstract

Interfacial stability of two-layer Couette flow was investigated experimentally in a channel bent into an annular ring. This paper is focused on the supercritical long-wave instability which arises for a broad range of flow parameters. Above the critical upper plate velocity, a slowly growing long wave appears with wavelength equal to the perimeter of the channel. Transients of this wave were studied within the theoretical frame of amplitude equations obtained from the long-wave interface equation. Near the onset of instability, the unstable fundamental harmonic is described by the Landau–Stuart equation, and the nonlinear dynamics of the harmonics closely follows the central and slaved modes analysis. For the higher upper plate velocity, harmonics gain some autonomy but they eventually are enslaved by the fundamental, through remarkable collapses of amplitudes and phase jumps leading to wave velocity and frequency locking. Dispersive effects play a crucial role in the nonlinear dynamics. Far from the threshold, the second harmonic becomes unstable and bistability appears: the saturated wave is dominated either by the fundamental harmonic, or by the even harmonics, after periodic energy exchange.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 303 , 25 November 1995 , pp. 23 - 53
Copyright
© 1995 Cambridge University Press

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