Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-18T23:58:04.564Z Has data issue: false hasContentIssue false
  • English
  • Français

On the stability of stratified viscous plane Couette flow. Part 2. Variable buoyancy frequency

Published online by Cambridge University Press:  11 April 2006

A. Davey  and
W. H. Reid
A. Davey
Affiliation:
School of Mathematics, University of Newcastle upon Tyne, England
W. H. Reid
Affiliation:
Department of Mathematics, University of Chicago, Illinois 60637
Get access Rights & Permissions [Opens in a new window]

Abstract

A statically stable stratification with buoyancy frequency N2(z) = z2 is found to cause large changes in the modal structure for viscous plane Couette flow (as compared with the case when N2(z) = 1) and it also has a strongly destabilizing effect on the flow. On minimizing with respect to both wavenumber and Richardson number, it is found that the flow is unstable if the Reynolds number is greater than about 183. A study of the Reynolds stress and vertical buoyancy flux shows that there is a large transfer of energy from the basic flow to the velocity disturbances and this is consistent with such a surprisingly low value of the minimum critical Reynolds number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 80 , Issue 3 , 2 May 1977 , pp. 527 - 534
Copyright
© 1977 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Banks, W. H. H., Drazin, P. G. & Zaturska, M. B. 1976 J. Fluid Mech. 75, 149.
Davey, A. & Reid, W. H. 1977 J. Fluid Mech. 80, 509.
Howard, L. N. 1961 J. Fluid Mech. 10, 509.
Howard, L. N. & Maslowe, S. A. 1973 Boundary-Layer Met. 4, 511.
Huppert, H. E. 1973 J. Fluid Mech. 57, 361.
Miles, J. W. 1961 J. Fluid Mech. 10, 496.
Stuart, J. T. 1963 In Laminar Boundary Layers (ed. L. Rcsenhead), pp. 492–579. Oxford: Clarendon Press.