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A note on the nonlinear development of the Batchelor–Nitsche instability

Published online by Cambridge University Press:  26 April 2006

M. R. E. Proctor
M. R. E. Proctor
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver St., Cambridge CB3 9EW, UK
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Abstract

The nonlinear development of the Batchelor–Nitsche instability (of a periodically stratified fluid) is considered, utilizing the disparity between vertical and horizontal scales of motion. The resulting evolution equation is used to show that the preferred pattern of convection takes the form of rolls, and that the motion evolves to larger and larger horizontal scales as time increases.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 254 , September 1993 , pp. 313 - 321
Copyright
© 1993 Cambridge University Press

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References

Batchelor, G. K. & Nitsche, J. M. 1991 Instability of stationary unbounded stratified fluid. J. Fluid Mech. 227, 357–391 (referred to herein as BN.)Google Scholar
Chapman, C. J. & Proctor, M. R. E. 1980 Nonlinear Rayleigh–Bénard convection between poorly conducting boundaries. J. Fluid Mech. 101, 759–782.Google Scholar
Jenkins, D. R. & Proctor, M. R. E. 1984 The transition from roll to square cell solutions in Rayleigh-Bénard convection. J. Fluid Mech. 139, 461–471.Google Scholar
Proctor, M. R. E. 1981 Planform selection by finite amplitude convection between poorly conducting slabs. J. Fluid Mech. 113, 469–485.Google Scholar
Proctor, M. R. E. & Holyer, J. Y. 1985 Planform selection in salt fingers. J. Fluid Mech. 168, 241–253.Google Scholar