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Long-wavelength instability of a line plume

Published online by Cambridge University Press:  21 April 2006

John R. Lister
John R. Lister
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
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Abstract

The stability of a steacty, laminar, immiscible, dense line plume falling through a fluid whose horizontal extent is much larger than the plume thickness is investigated. It is shown analytically that the primary flow is linearly unstable in the limit of large wavelength and, if surface tension is negligible, is also unstable in the limit of small Reynolds number. A rich variety of modes of perturbation exist, characterized by a range of balances on different lengthscales between diffusion, advection and propagation of vorticity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 175 , February 1987 , pp. 413 - 428
Copyright
© 1987 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.
Hickox, C. E. 1971 Stability of two fluids in a pipe. Phys. Fluids 14, 251.Google Scholar
Hinch, E. J. 1984 A note on the mechanism of the instability at the interface between two shearing fluids. J. Fluid Mech. 144, 463.Google Scholar
Hooper, A. P. 1985 Long wave instability at the interface between two viscous fluids: thin layer effects. Phys. Fluids 28, 1613.Google Scholar
Hooper, A. P. 1986 Shear flow instability due to a wall and a viscosity discontinuity at the interface. J. Fluid Mech. (submitted).Google Scholar
Hooper, A. P. & Boyd, W. G. C. 1983 Shear-flow instability at the interface between two viscous fluids. J. Fluid Mech. 128, 507.Google Scholar
Huppert, H. E., Sparks, R. S. J., Whitehead, J. A. & Hallworth, M. A. 1986 The replenishment of magma chambers by light inputs. J. Geophys. Res. 91, 6113.Google Scholar
Joseph, D. D., Renardy, M. & Renardy, Y. 1984 Instability of the flow of two immiscible liquids with different viscosities in a pipe. J. Fluid Mech. 141, 309.Google Scholar
Yih, C.-S. 1963 Stability of liquid flow down an inclined plane. Phys. Fluids 6, 321.Google Scholar
Yih, C.-S. 1967 Instability due to viscosity stratification. J. Fluid Mech. 27, 337.Google Scholar