Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-18T08:45:31.929Z Has data issue: false hasContentIssue false
  • English
  • Français

Lee waves in stratified flows with simple harmonic time dependence

Published online by Cambridge University Press:  29 March 2006

T. H. Bell
T. H. Bell
Affiliation:
Ocean Sciences Division, Naval Research Laboratory, Washington, D.C. 20375
Get access Rights & Permissions [Opens in a new window]

Abstract

The process of internal gravity wave generation by the simple harmonic flow (U = U0, cos ω0t) of a stably stratified fluid (Brunt–Väisälä frequency N) over an obstacle is investigated in some detail. Attention is primarily directed to the behaviour of the solution in various limiting cases, and to estimating the flux of energy into the internal wave field. In general, waves are generated not only at the fundamental frequency ω0, but also at all of its harmonics. But, for values of ω0/N greater than about one half, the waves of fundamental frequency are dominant. For values of ω0/N, less than about one half, the quasi-static approximation, in which the problem is considered as a slowly-varying version of the classical lee wave problem, is found to provide a viable estimate for the wave field. The general solution is found to compare favourably with the limited available experimental data.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 67 , Issue 4 , 25 February 1975 , pp. 705 - 722
Copyright
© 1975 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

Baines, P. G. 1973 The generation of internal tides by flat-bump topography. Deep-Sea Res., 20, 179–205.Google Scholar
Bell, T. H. 1973 Internal wave generation by deep ocean flows over abyssal topography. Ph.D. thesis, The Johns Hopkins University.
Bretherton, F. P. 1971 The general linearized theory of wave propagation. Mathematical Problems in the Geophysical Sciences (ed. W. H. Reid), vol. 1, pp. 61–102. Am. Math. Soc.
Browand, F. K. & Winant, C. D. 1972 Blocking ahead of a cylinder moving in a strati-fied fluid: an experiment. Geophys. Fluid Dyn., 4, 29–53.Google Scholar
Budden, K. G. 1961 Radio Waves in the Ionosphere. Cambridge University Press.
Cartwright, D. E. 1959 On submarine sand — waves and tidal lee-waves. Proc. Roy. Soc. A 253, 218–241.Google Scholar
Cox, C. & Sandstrom, H. 1962 Coupling of internal and surface waves in water of variable depth. J. Ocean. Soc. Japan, 20, 499–513.Google Scholar
Erdélyi, A., Magnus, W., Oberhettincer, F. & Tricomi, F. G. 1953 Higher Transcendental Functions, vol. 1. McGraw-Hill.
Erdélyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F. G. 1954 Tables of Integral Transforms, vol. 1. McGraw-Hill.
Görtler, H. 1943 Über eine Schwingungserscheinung in Flussigkeiten mit stabiler
Dichteschichtung. 2. angew. Math. Mech., 23 65–71.
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Hurley, D. G. 1969 The emission of internal waves by vibrating cylinders. J. Fluid Mech.Google Scholar
Lee, C. Y. 1972 Long nonlinear internal waves and quasi — steady lee waves. Ph.D. thesis, Massachusetts Institute of Technology.
Lighthill, M. J. 1967 On waves generated in dispersive systems by travelling forcing effects, with applications to the dynamics of rotating fluids. J. Fluid Mech., 27, 725–752.Google Scholar
Lilly, D.K. 1972 Wave momentumflux: a GARP problem. Bull. Arm Meteor. Soc., 53, 17–23.Google Scholar
Miles, J. W. 1969 Waves and wave drag in stratified flows. Applied Mechanics: Proc. 12th Int. Cong. Appl. Mech. (ed. M. Hetenyi & W. G. Vincenti), pp. 50–76. Springer.
Miles, J. W. 1971 Upstream boundary layer separation in stratified flow. J. Fluid Mech., 48, 791–800.Google Scholar
Miles, J. W. & Huppert, H. E. 1969 Lee waves in a stratified flow. Part 4. Perturbation approximations. J. Fluid Mech. 35, 497–525.Google Scholar
Mork, M. 1968 On the formation of internal waves caused by tidal flow over a bottom irregularity. Geophys. Inst. Univ. Bergen.Google Scholar
Mowbray, D. E. & Rarity, B. S. H. 1967 A theoretical and experimental investigation of the phase configuration of internal waves of small amplitude in a density stratified liquid. J. Fluid Mech., 28, 1–16.Google Scholar
Rattray, M., Dworski, J. & Kovala, P. 1969 Generation of long internal waves a t the continental slope. Deep-Sea Res. (Suppl.), 16, 179–195.Google Scholar
Watson, G. N. 1966 A Treatise on the Theory of Bessel Functions. 2nd edn. Cambridge University Press.
Zeytounian, R. Kh. 1969a Phénomènes d'ondes dans les écoulements stationnaires d'un fluide stratifié non visqueux: I. Modéles théoriques. J. Mécanique, 8, 239–263.Google Scholar
Zeytounian, R. Kh. 1969b Phénomènes d'ondes dans les Bcoulemerits stationnaires d'un fluide stratifié non visqueux: II. Applications météorologiques: ondes de refief dam une atmosphère barocline. J. Mécanique, 8, 335–355.Google Scholar