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Stability of a stratified fluid with a vertically moving sidewall


We present the results of a combined theoretical and experimental study of the stability of a uniformly stratified fluid bounded by a sidewall moving vertically with constant velocity. This arrangement is perhaps the simplest in which boundary effects can drive instability and, potentially, layering in a stratified fluid. Our investigations reveal that for a given stratification and diffusivity of the stratifying agent, the sidewall boundary-layer flow becomes linearly unstable when the wall velocity exceeds a critical value. The onset of instability is clearly observed in the experiments, and there is good quantitative agreement with some predictions of the linear stability analysis.

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Dauchot O. & Daviaud F. 1995 Finite-amplitude perturbation and spots growth-mechanism in plane couette-flow. Phys. Fluids 7, 335343.
Finlayson B. A. 1972 The Method of Weighted Residuals and Variational Principles, pp. 151203. Academic.
Grossmann S. 2000 The onset of sheer flow turbulence. Rev. Mod. Phys. 72 (2), 603618.
Hart J. E. 1971 Sideways diffusive instability. J. Fluid Mech. 49, 279288.
Huppert H. E. & Turner J. S. 1980 Ice blocks melting into a salinity gradient. J. Fluid Mech. 100, 167384.
Kerr O. S. 2000 The criteria for the onset of double-diffusive instabilities at a vertical boundary. Phys. Fluids 12 (12), 32893292.
Linden P. & Weber F. 1977 The formation of layers in a double-diffusive system with a sloping boundary. J. Fluid Mech. 81, 757773.
Mendenhall C. E. & Mason M. 1923 The stratified subsidence of fine particles. Proc. Natl Acad. Sci. 9, 199202.
Oster G. 1965 Density gradients. Sci. Am. 213, 70.
Paliwal R. C. & Chen C. F. 1979 Double-diffusive instability in an inclined fluid layer. Part 2. stability analysis. J. Fluid Mech. 98, 769785.
Peacock T., Blanchette F. & Bush J. W. M. 2005 The stratified Boycott effect. J. Fluid Mech. 529, 3349.
Robinson R. M. & McEwan A. D. 1975 Instability of a periodic boundary-layer in a stratified fluid. J. Fluid Mech. 68, 41.
Standing R. G. 1971 The rayleigh problem for a slightly diffusive density-stratified fluid. J. Fluid Mech. 48, 673688.
Sutherland B. R., Dalziel S. B., Hughes G. O. & Linden P. F. 1999 Visualisation and measurement of internal waves by ‘synthetic schlieren’. Part 1. Vertically oscillating cylinder. J. Fluid Mech. 390, 93126.
Tanny J. & Tsinober A. B. 1988 The dynamics and structure of double-diffusive layers in sidewall heating experiments. J. Fluid Mech. 196, 151160.
Thangam S., Zebib A. & Chen C. F. 1981 Transition fronmm shear to sideways diffusive instability in s vertical slot. J. Fluid Mech. 112, 151160.
Thorpe S. A. 1969 The effect of horizontal gradients on thermohaline convection. J. Fluid Mech. 38, 375400.
Turner J. S. 1985 Multicomponent convection. Annu. Rev. Fluid. Mech. 17, 1144.
Weistein S. J. & Ruschak K. J. 2004 Coating rows. Annu. Rev. Fluid Mech. 36, 2953.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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