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Oscillatory Kelvin–Helmholtz instability. Part 2. An experiment in fluids with a large viscosity contrast

Published online by Cambridge University Press:  23 March 2011

HARUNORI N. YOSHIKAWA  and
JOSÉ EDUARDO WESFREID
HARUNORI N. YOSHIKAWA*
Affiliation:
Physique et Mécanique des Milieux Hétérogènes (PMMH), UMR 7636 CNRS – ESPCI – UPMC Université de Paris 06 – UPD Université de Paris 07 10, rue Vauquelin 75231 Paris CEDEX 5, France
JOSÉ EDUARDO WESFREID
Affiliation:
Physique et Mécanique des Milieux Hétérogènes (PMMH), UMR 7636 CNRS – ESPCI – UPMC Université de Paris 06 – UPD Université de Paris 07 10, rue Vauquelin 75231 Paris CEDEX 5, France
*
†Present address: Laboratoire J.-A. Dieudonné, Université de Nice Sophia-Antipolis, Parc Valrose – 06108 Nice CEDEX 2, France. Email address for correspondence: harunori@unice.fr
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Abstract

The stability of two-layer oscillatory flows was studied experimentally in a cylindrical container with a vertical axis. Two superposed immiscible liquids, differing greatly in viscosity, were set in relative oscillatory motion by alternating container rotation. Waves arising beyond a threshold were observed in detail for small oscillation frequencies ranging from 0.1 to 6 Hz. Measurements were performed on the growth rate and the wavenumber of these waves. The instability threshold was determined from the growth rate data. It was found that the threshold and the wavenumber varied with the frequency. In particular, significantly lower thresholds and longer waves were found than those predicted by the inviscid theory of the oscillatory Kelvin–Helmholtz instability. Favourable agreement with the predictions of an existing viscous theory for small oscillation amplitude flows indicates the important role of viscosity, even at the highest frequency, and suggests a similar mechanism behind the instability as that for the short wave instability in steady Couette flows. A semi-numerical stability determination for finite amplitude flows was also performed to improve the prediction in experiments with a frequency lower than 1 Hz.

JFM classification

Boundary Layers: Boundary layer stability Geophysical and Geological Flows: Coastal engineering Nonlinear Dynamical Systems: Pattern formation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 675 , 25 May 2011 , pp. 249 - 267
Copyright
Copyright © Cambridge University Press 2011

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Yoshikawa et al. supplementary material

Waves developing on an interface in a two-layer oscillatory flow in fluids with a large viscosity contrast (upper layer: silicone oil of 10000 mm2/s; lower layer: water). The oscillatory flow is induced by alternating rotation of a cylindrical container, in which the fluids are superposed. A transition from sinusoidal to non-sinusoidal waves is observed during the formation of oil fingers. The latter waves grow more rapidly than the former ones until the saturation. (The movie window has 192 mm of width and 38 mm of height in the real size. The movie plays 2.5 times faster than the real time.).

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