Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-05-01T14:34:11.812Z Has data issue: false hasContentIssue false
  • English
  • Français

Three-dimensional wave instability near a critical level

Published online by Cambridge University Press:  26 April 2006

K. B. Winters  and
E. A. D’Asaro
K. B. Winters
Affiliation:
Department of Applied Mathematics and Applied Physics Laboratory, University of Washington, Seattle, WA 98105, USA
E. A. D’Asaro
Affiliation:
Department of Oceanography and Applied Physics Laboratory, University of Washington, Seattle, WA 98105, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The behaviour of internal gravity wave packets approaching a critical level is investigated through numerical simulation. Initial-value problems are formulated for both small- and large-amplitude wave packets. Wave propagation and the early stages of interaction with the mean shear are two-dimensional and result in the trapping of wave energy near a critical level. The subsequent dynamics of wave instability, however, are fundamentally different for two- and three-dimensional calculations. Three-dimensionality develops by transverse convective instability of the two-dimensional wave. The initialy two-dimensional flow eventually collapses into quasi-horizontal vortical structures. A detailed energy balance is presented. Of the initial wave energy, roughly one third reflects, one third results in mean flow acceleration and the remainder cascades to small scales where it is dissipated. The detailed budget depends on the wave amplitude, the amount of wave reflection being particularly sensitive.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 272 , 10 August 1994 , pp. 255 - 284
Copyright
Copyright © Cambridge University Press 1994

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

Breeding, R. J. 1971 A nonlinear investigation of critical levels for internal atmospheric gravity waves. J. Fluid Mech. 50, 545–563.Google Scholar
Bretherton, F. P. 1966 The propagation of groups of internal gravity waves in a shear flow. Q. J. R. Met. Soc. 92, 466–480.Google Scholar
Domaradzki, J. A., Metcalfe, R. W., Rogallo, R. S. & Riley, J. J. 1987 Analysis of subgrid eddy viscosity with use of results from direct numerical simulations. Phys. Rev. Lett. 58, 547–550.Google Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.Google Scholar
Farge, M. 1987 Dynamique non lineaire des ondes et des tourbillons dans les equations de Saint-Venant. These de Doctorat d’Etat et Sciences Mathematique, Univesite Paris VI.Google Scholar
Fritts, D. C. 1982 The transient critical level interaction in a Boussinesq fluid. J. Atmos. Sci. 87, 7797–8016.Google Scholar
Fritts, D. C. & Geller, M. A. 1976 Viscous stabilization of gravity wave critical level flows. J. Atmos. Sci. 33, 2276–2284.Google Scholar
Hazel, P. 1967 The effect of viscosity and heat conduction on internal gravity waves at a critical level. J. Fluid Mech. 30, 775–783.Google Scholar
Henyey, F. S., Wright, J. & Flatte, S. 1984 Energy and action flow through the internal wavefield: an eikonal approach. J. Geophys. Res. 91, 8487–8495.Google Scholar
Koop, C. G. 1981 A preliminary investigation of the interaction of internal gravity waves with a steady-shearing motion. J. Fluid Mech. 113, 347–386.Google Scholar
Koop, C. G. & McGee, B. 1986 Measurements of internal gravity waves in a continuously stratified shear flow. J. Fluid Mech. 172, 453–480.Google Scholar
Lelong, M. P. 1989 Weakly nonlinear internal wave/vortical mode interactions in stably-stratified flows. PhD thesis, University of Washington.Google Scholar
Lin, C. L., Ferziger, K. H., Koseff, J. R. & Monismith, S. G. 1993 Simulation and stability of two dimensional internal gravity waves in a stratified shear flow. Dyn. Atmos. Oceans 19, 325–366.Google Scholar
Lin, J. T. & Pao, Y. H. 1979 Wakes in stratified fluids. Ann. Rev. Fluid Mech. 11, 317–338.Google Scholar
Staquet, C. & Riley, J. J. 1989a A numerical study of a stably-stratified mixing layer. In Selected Papers from the Sixth Symposium on Turbulent Shear Flows, Springer, Berlin, pp. 381–397.Google Scholar
Staquet, C. & Riley, J. J. 1989b On the velocity field associated with potential vorticity. Dyn. Atmos. Oceans 14, 93–123.Google Scholar
Thorpe, S. A. 1981 An experimental study of critical layers. J. Fluid Mech. 193, 321–344.Google Scholar
Thorpe, S. A. 1987 Transitional phenomena and the development of turbulence in stratified fluids: A review. J. Geophys. Res. 92, 5231–5248.Google Scholar
Walterscheid, R. L. & Schubert, G. 1990 Nonlinear evolution of an upward propagating gravity wave: overturning, convection, transience and turbulence. J. Atmos. Sci. 49, 101–125.Google Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.Google Scholar
Winters, K. B. & D’Asaro, E. A. 1989 Two dimensional instability of finite amplitude internal gravity wave packets near a critical level. J. Geophys. Res. 94, 12709–12719.Google Scholar
Winters, K. B. & D’Asaro, E. A. 1991 Diagnosing diapycnal mixing. In Proc. Hawaiian Winter Workshop: Dynamics of Oceanic Internal Gravity Waves, University of Hawaii at Manoa, pp. 279–294.Google Scholar
Winters, K. B. & D’Asaro, E. A. 1994 Available potential energy and mixing in density-stratified fluids. J. Fluid Mech. (submitted).Google Scholar
Winters, K. B. & Riley, J. J. 1992 Instability of internal waves near a critical level. Dyn. Atmos. Oceans 16, 249–278.Google Scholar