Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-08T05:36:23.836Z Has data issue: false hasContentIssue false

A preliminary investigation of the interaction of internal gravity waves with a steady shearing motion

Published online by Cambridge University Press:  20 April 2006

C. Gary Koop
Affiliation:
Fluid Mechanics Department, TRW Defense and Space Systems Group, Redondo Beach, California 90278

Abstract

Preliminary experimental results are presented which describe the interaction of an internal-wave field with a steady shearing motion. The results are primarily qualitative and presented in the form of photographs of shadowgraph images. Several internal-wave sources are used, and both critical- and non-critical-layer flows are examined. The results of these observations are interpreted in terms of several existing theories. For critical-layer flows the primary result is that virtually none of the internal-wave momentum flux penetrates the critical-level region, and under certain conditions a critical-layer instability develops resulting in the generation of turbulence. Such wave-induced turbulence is also observed for certain non-critical-layer flows and is believed to be the result of a convective instability.

Type
Research Article
Copyright
© 1981 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

Beland, M. 1978 The evolution of a nonlinear Rossby-wave critical layer: effect of viscosity. J. Atmos. Sci. 35, 1802.Google Scholar
Booker, J. & Bretherton, F. 1967 The critical layer for internal gravity waves in a shear flow. J. Fluid Mech. 27, 513.Google Scholar
Bretherton, F. 1966 The propagation of groups of internal gravity waves in a shear flow. Quart. J. Roy. Met. Soc. A 92, 466.Google Scholar
Browand, F. & Winant, C. 1972 Blocking ahead of a cylinder moving in a stratified fluid: an experiment. Geophys. Fluid Dyn. 4, 29.Google Scholar
Brown, S. & Stewartson, K. 1980 On the nonlinear reflection of a gravity wave at a critical layer. J. Fluid Mech. 100, 577.Google Scholar
Dickinson, R. 1970 Development of a Rossby-wave critical level. J. Atmos. Sci. 27, 627.Google Scholar
Fritts, D. 1978 The nonlinear gravity-wave/critical-level interaction. J. Atmos. Sci. 35, 397.Google Scholar
Fritts, D. 1979 The excitation of radiating waves and Kelvin — Helmholtz instabilities by the gravity-wave critical-level interaction. J. Atmos. Sci. 26, 12.Google Scholar
Fritts, D. & Geller, M. 1976 Viscous stabilization of gravity-wave critical-level flows. J. Atmos. Sci. 33, 2276.Google Scholar
Geller, M., Tanaka, H. & Fritts, D. 1975 Production of turbulence in the vicinity of critical layers for internal gravity waves. J. Atmos. Sci. 32, 2125.Google Scholar
Grimshaw, R. 1974 Internal gravity waves in a slow varying dissipative medium. Geophys. Fluid Dyn. 6, 131.Google Scholar
Haberman, R. 1972 Critical layers in a parallel flow. Stud. Appl. Math. 51, 139.Google Scholar
Hazel, P. 1967 The effect of viscosity and heat conduction on internal gravity waves at a critical level. J. Fluid Mech. 30, 775.Google Scholar
Jones, W. & Houghton, D. 1971 The coupling of momentum between internal gravity waves and mean flow: a numerical study. J. Atmos. Sci. 28, 604.Google Scholar
Long, R. 1955 Some aspects of the flow of stratified fluid. III. Continuous density gradients. Tellus 7, 342.Google Scholar
Lyra, G. 1943 Theorie der stationären Leewellenströmung in freier Atmosphäre. Z. angew. Math. Mech. 23, 1.Google Scholar
Mager, R. 1974 Internal gravity waves generated by a moving source in a stratified fluid. Denver Research Institute Rep. No. DRI MS-R-7502, Univ. of Denver, Denver, Colorado.
Maslowe, S. 1972 The generation of clear-air turbulence by nonlinear waves. Stud. Appl. Math. 51, 1.Google Scholar
Mowbray, D. & Rarity, B. 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.Google Scholar
Odell, G. & Kovasznay, L. 1971 A new type of water channel with density stratification. J. Fluid Mech. 50, 535.Google Scholar
Orlanski, I. & Bryan, K. 1969 Formation of the thermocline step structure by large-amplitude internal gravity waves. J. Geophys. Res. 74, 6975.Google Scholar
Orlanski, I. 1972 On the breaking of standing internal gravity waves. J. Fluid Mech. 54, 577.Google Scholar
Phillips, O. 1966 Dynamics of the Upper Ocean. Cambridge University Press.
Quency, P. 1948 The problem of air flow over mountains: a summary of theoretical studies Bull. Am. Met. Soc. 29, 16.Google Scholar
Sanford, T. 1975 Observation of the vertical structure of internal waves. J. Geophys. Res. 80, 3861.Google Scholar
Sawyer, J. 1960 A numerical calculation of the displacements of a stratified airstream crossing. a ridge of small height. Quart. J. Roy. Met. Soc. 86, 326.Google Scholar
Stewartson, K. 1978 The evolution of the critical level of a Rossby wave. Geophys. Astrophys. Fluid Dyn. 9, 185.Google Scholar
Thorpe, S. 1978 On the shape and breaking of internal gravity waves in a shear flow. J. Fluid Mech. 85, 7.Google Scholar
Turner, J. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
Warn, T. & Warn, H. 1978 The evolution of a nonlinear critical layer. Stud. Appl. Math. 59, 37.Google Scholar
Woods, J. 1968 Wave induced shear instability in the Summer thermocline. J. Fluid Mech. 32, 791.Google Scholar