Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-13T01:26:29.339Z Has data issue: false hasContentIssue false
  • English
  • Français

Lee waves in a stratified flow Part 1. Thin barrier

Published online by Cambridge University Press:  28 March 2006

John W. Miles
John W. Miles
Affiliation:
Institute of Geophysics and Planetary Physics University of California, La Jolla
Get access Rights & Permissions [Opens in a new window]

Abstract

The lee-wave amplitudes and wave drag for a thin barrier in a two-dimensional stratified flow in which the upstream dynamic pressure and density gradient are constant (Long's model) are determined as functions of barrier height and Froude number for a channel of finite height and for a half-space. Variational approximations to these quantities are obtained and validated by comparison with the earlier results of Drazin & Moore (1967) for the channel and with the results of an exact solution for the half-space, as obtained through separation of variables. An approximate solution of the integral equation for the channel also is obtained through a reduction to a singular integral equation of potential theory. The wave drag tends to increase with decreasing wind speed, but it seems likely that the flow is unstable in the region of high drag. The maximum attainable drag coefficient consistent with stable lee-wave formation appears to be roughly two and almost certainly less than three.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 32 , Issue 3 , 24 May 1968 , pp. 549 - 567
Copyright
© 1968 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

Abramowitz, M. & Stegun, I. 1964 Handbook of Mathematical Functions. Washington: National Bureau of Standards.
Blumen, W. 1965 A random model of momentum flux by mountain waves Geofys. Publ. Norske Vid.-Acad. Oslo 26, no. 2.Google Scholar
Dbazin, P. G. & Moore, D. W. 1967 Steady two-dimensional flow of fluid of variable density over an obstacle J. Fluid Mech. 28, 353–70.Google Scholar
Jones, O. K. 1967 Some problems in the steady two-dimensional flow of an incompressible, inviscid and stably stratified fluid. Ph.D. Thesis, University of Bristol.
Long, R. R. 1953 Some aspects of the flow of stratified fluids. I. A theoretical investigation Tellus, 5, 42–58.Google Scholar
Long, R. R. 1955 Some aspects of the flow of stratified fluids. III. Continuous density gradients Tellus, 7, 341–57.Google Scholar
Marcuvitz, N. 1951 Waveguide Handbook. New York: McGraw-Hill.
Miles, J. W. 1959 The Potential Theory of Unsteady Supersonic Flow. Cambridge University Press.
Miles, J. W. 1967 Surface-wave scattering matrix for a shelf J. Fluid Mech. 28, 755–68.Google Scholar
Rayleigh, LORD 1897 On the passage of waves through apertures in plane screens and allied problems. Phil. Mag. 43, 259–72; Scientific Papers, 4, 283–96 (see especially first paragraph, p. 288).Google Scholar
Sawyer, J. S. 1959 The introduction of the effects of topography into methods of numerical forecasting Quart. J.R. meteor. Soc. 85, 31–43.Google Scholar
Schooley, A. H. & Stewart, R. W. 1963 Experiments with a self-propelled body submerged in a fluid with a vertical density gradient J. Fluid Mech. 15, 83–96.Google Scholar
Soehngen, H. 1939 Die Lösungen der Integralgleichung ∞ und deren Anwendung in der Tragflügel theorie. Math. Z. 45, 245–64.Google Scholar
VAN DYKE, M. D. 1964 Perturbation Methods in Fluid Mechanics. New York: Academic Press.
Yih, C.-S. 1965 Dynamics of Nonhomogeneous Fluids. New York: Macmillan.