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On the instability of the flow in an oscillating tank of fluid

Published online by Cambridge University Press:  26 April 2006

Philip Hall
Philip Hall
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL, UK
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Abstract

The instability of a viscous fluid inside a rectangular tank oscillating about an axis parallel to the largest face of the tank is investigated in the linear regime. The flow is shown to be unstable to both longitudinal roll and standing wave instabilities. The particular cases of low and high oscillation frequencies are discussed in detail. The relationship between the roll instability and convective or centrifugal instabilities in unsteady boundary layers is discussed. The eigenvalue problems associated with the roll and standing wave instabilities are solved using Floquet theory and a combination of numerical and asymptotic methods. The results obtained are compared to the recent experimental investigation of Bolton & Maurer (1994) which indeed provided the stimulus for the present investigation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 268 , 10 June 1994 , pp. 315 - 331
Copyright
© 1994 Cambridge University Press

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References

Akhavan, R., Kamm, R. D. & Shapiro, A. H. 1991a An investigation of transition to turbulence in bounded oscillatory Stokes flows. Part 1. Experiments. J. Fluid Mech. 225, 395–422.Google Scholar
Akhavan, R., Kamm, R. D. & Shapiro, A. H. 1991b An investigation of transition to turbulence in bounded oscillatory Stokes flows. Part 2. Numerical simulations. J. Fluid Mech. 225, 423–444.Google Scholar
Bolton, E. W. & Maurer, J. 1994 A new roll type instability in an oscillating fluid plane. J. Fluid Mech. 268, 293–313 (referred to herein as BM).Google Scholar
Gresho, P. M. & Sani, R. L. 1970 The effects of gravity modulation on the stability of a heated fluid layer. J. Fluid Mech. 40, 783–806.Google Scholar
Hall, P. 1978 The linear stability of flat Stokes layers. Proc. R. Soc. Lond. A 359, 151–166.Google Scholar
Hall, P. 1981 Centrifugal instability of a Stokes layer: subharmonic destabilization of the Taylor vortex mode. J. Fluid Mech. 105, 523–530.Google Scholar
Hall, P. 1984 On the stability of the unsteady boundary layer on a cylinder oscillating transversely in a viscous fluid. J. Fluid Mech. 146, 347–367.Google Scholar
Hall, P. 1985 On the instability of time-periodic flows. In Instability of Spatially and Temporally Varying Flows (ed. M. Hussaini & P. Vogt), pp. 206–224. Springer.
Hall, P. & Horseman, N. J. 1991 The inviscid secondary instability of fully nonlinear vortex structures in growing boundary layers. J. Fluid Mech. 232, 357–375.Google Scholar
Kerczek, C. von & Davis, S. H. 1974 Linear stability theory of oscillatory Stokes layers. J. Fluid Mech. 62, 753–773.Google Scholar
Papageorgiou, D. 1987 Stability of unsteady viscous flow in a curved pipe. J. Fluid Mech. 182, 209–233.Google Scholar
Park, K., Barenghi, C. & Donnelly, R. J. 1980 Subharmonic destabilization of Taylor vortices near an oscillating cylinder. Phys. Lett. 78A, 152–154.Google Scholar
Seminara, G. & Hall, P. 1976 Centrifugal instability of a Stokes layer: linear theory. Proc. R. Soc. Lond. A 350, 299–316.Google Scholar