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Upstream boundary-layer separation in stratified flow

Published online by Cambridge University Press:  29 March 2006

John W. Miles
John W. Miles
Affiliation:
Institute of Geophysics and Planetary Physics
Also Department of Aerospace and Mechanical Engineering Sciences.
University of California, La Jolla, California 92037
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Abstract

Stratified, inviscid channel flow over a thin barrier or into an abrupt contraction is considered on the hypotheses that the upstream dynamic pressure and density gradient are constant (Long's model) for those parametric régimes in which the hypotheses are tenable for finite-amplitude disturbances, namely k < 2 for the barrier and k < 1 for the contraction, where k = NH/πU is an inverse Froude number based on the Vaisälä frequency N, the channel height H, and the upstream velocity U. Reverse flow in the neighbourhood of the forward stagnation point, which implies the formation of an upstream separation bubble, is found for certain critical ranges of k. The maximum barrier height for which the dominant lee-wave mode can exist without reversed flow either upstream or downstream of the barrier is 0·34H. The limiting case of a half space is considered briefly, and forward separation is found for κ = Nh/U > κs, where κs = 2·05 for a thin barrier and 1·8 for a semi-circular barrier. The corresponding values for reverse flow in the lee-wave field are κc = 1·73 and 1·3, respectively.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 48 , Issue 4 , 27 August 1971 , pp. 791 - 800
Copyright
© 1971 Cambridge University Press

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References

Debler, W. R. 1959 Stratified flow into a line sink J. Engng Mech. Div., Proc. ASCE 85, 51–65.Google Scholar
Jones, O. K. 1970 The flow of a stratified fluid over a vertical step Tellus, 23, 481–492.Google Scholar
Long, R. R. 1953 Some aspects of the flow of stratified fluids. I. A theoretical investigation Tellus, 5, 52–58.Google Scholar
Long, R. R. 1955 Some aspects of the flow of stratified fluids. III. Continuous density gradients Tellus, 7, 341–57.Google Scholar
Maxworthy, T. 1970 The flow created by a sphere moving along the axis of a rotating, slightly viscous fluid J. Fluid Mech. 40, 453–80.Google Scholar
McIntyre, M. E. 1971 On Long's hypothesis of no upstream influence in uniformly stratified or rotating flow. J. Fluid Mech. (in the press).Google Scholar
Miles, J. W. 1968a Lee waves in a stratified flow. Part 1. Thin barrier J. Fluid Mech. 32, 549–67.Google Scholar
Miles, J. W. 1968b (With appendix by H. E. Huppert.) Lee waves in a stratified flow. Part 2. Semi-circular obstacle J. Fluid Mech. 33, 803–14.Google Scholar
Miles, J. W. 1971 Boundary-layer separation on a sphere in a rotating flow J. Fluid Mech. 45, 513–26.Google Scholar
Milne-Thomson, L. M. 1960 Theoretical Hydrodynamics. New York: Macmillan.
National Bureau of Standards 1951 Tables Relating to Mathieu Functions. New York: Columbia University Press.
Wong, K. K. & Kao, T. W. 1970 Stratified flow over extended obstacles. J. Atmos. Sci. 27, 884–889.Google Scholar