Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-28T03:49:01.799Z Has data issue: false hasContentIssue false
  • English
  • Français

Energy stability of the Ekman boundary layer

Published online by Cambridge University Press:  29 March 2006

Joseph J. Dudis  and
Stephen H. Davis
Joseph J. Dudis
Affiliation:
The Johns Hopkins University, Baltimore, Maryland
Stephen H. Davis
Affiliation:
The Johns Hopkins University, Baltimore, Maryland
Get access Rights & Permissions [Opens in a new window]

Abstract

The critical value RE of the Reynolds number R is predicted by the application of the energy theory. When R < RE, the Ekman layer is the unique steady solution of the Navier-Stokes equations and the same boundary conditions, and is, further, stable in a slightly weaker sense than asymptotically stable in the mean. The critical value RE is determined by numerically integrating the relevant Euler-Lagrange equations. An analytic lower bound to RE is obtained. Comparisons are made between RE and RL, the critical value of R according to linear theory, in order to demark the region of parameter space, RE < R < RL, in which subcritical instabilities are allowable.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 47 , Issue 2 , 31 May 1971 , pp. 405 - 413
Copyright
© 1971 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

Barcilon, V. 1965 Tellus, 17, 53.
Dudis, J. J. & Davis, S. H. 1970 J. Fluid Mech. 47, 381.
Faller, A. J. 1963 J. Fluid Mech. 15, 560.
Faller, A. J. & Kaylor, R. E. 1966 J. Atm. Sci. 23, 466.
Gill, A. E. & Davey, A. 1969 J. Fluid Mech. 35, 775.
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Lilly, D. K. 1966 J. Atmos. Sci. 23, 481.
Tatro, P. R. & Mollö-Christensen, E. L. 1967 J. Fluid Mech. 28, 531.
Veronis, G. 1967 Tellus, 19, 326.