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Lee waves in a stratified flow Part 1. Thin barrier

  • John W. Miles (a1)


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.



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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.
Dbazin, P. G. & Moore, D. W. 1967 Steady two-dimensional flow of fluid of variable density over an obstacle J. Fluid Mech. 28, 35370.
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, 4258.
Long, R. R. 1955 Some aspects of the flow of stratified fluids. III. Continuous density gradients Tellus, 7, 34157.
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, 75568.
Rayleigh, LORD 1897 On the passage of waves through apertures in plane screens and allied problems. Phil. Mag. 43, 25972; Scientific Papers, 4, 283–96 (see especially first paragraph, p. 288).
Sawyer, J. S. 1959 The introduction of the effects of topography into methods of numerical forecasting Quart. J.R. meteor. Soc. 85, 3143.
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, 8396.
Soehngen, H. 1939 Die Lösungen der Integralgleichung ∞ und deren Anwendung in der Tragflügel theorie. Math. Z. 45, 24564.
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.
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Lee waves in a stratified flow Part 1. Thin barrier

  • John W. Miles (a1)


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