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A new roll-type instability in an oscillating fluid plane

Published online by Cambridge University Press:  26 April 2006

Edward W. Bolton  and
J. Maurer
Edward W. Bolton
Affiliation:
Department of Geology and Geophysics, Yale University, PO Box 208109, New Haven, CT 06520–8109, USA Département de Physique, Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cédex 05, France
J. Maurer
Affiliation:
Département de Physique, Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cédex 05, France
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Abstract

A new roll-type instability has been discovered experimentally. When fluid between two closely spaced, parallel plates is oscillated about an axis midway between the plates, it exhibits an instability that takes the form of longitudinal rolls aligned perpendicular to the axis of rotation. The basic-state oscillatory shear flow, before the onset of rolls, may be viewed as driven by the $\dot{\bm \Omega}\times \hat{\bm r}$ term of the Navier–Stokes equation in the oscillatory reference frame. A regime diagram is presented in a parameter space defined by the maximum amplitude of angular oscillation, α, and the non-dimensional frequency, Φ = ωd2/ν. The equilibrium wavelength of the rolls scales with d, the gap spacing between the plates, and it increases as Φ increases. Supercritical to a weak-roll onset, an abrupt transition to stronger roll amplitude occurs. Photographs of the cell after an impulsive start show the roll development and initial increase in roll wavelength. A variety of phenomena are observed, including wavelength selection via defect creation and elimination, front propagation, secondary wave instabilities, and the transition to turbulence. We also present solutions of the Navier–Stokes equation for the basic-state shear flow in a near-axis approximation. We develop a simple resonance model which shows some promise in understanding the low-α, high-Φ behaviour of strong rolls. A theoretical analysis of this instability is presented by Hall (1994).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 268 , 10 June 1994 , pp. 293 - 313
Copyright
© 1994 Cambridge University Press

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