Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2025-01-04T04:50:03.418Z Has data issue: false hasContentIssue false
  • English
  • Français

Explosive resonant triads in a continuously stratified shear flow

Published online by Cambridge University Press:  26 April 2006

Janet M. Becker  and
Roger H. J. Grimshaw
Janet M. Becker
Affiliation:
Physical Oceanography Research Division, University of California, San Diego, La Jolla, CA 92093-0230, USA
Roger H. J. Grimshaw
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

A variational formulation for three-dimensional waves in a continuously stratified shear flow is used to derive the equations governing a resonant triad of waves. It is argued that in general, critical layers are necessary for the existence of explosive resonant triads.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 257 , December 1993 , pp. 219 - 228
Copyright
© 1993 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

Cairns, R. A. 1979 The role of negative energy waves in some instabilities of parallel flows. J. Fluid Mech. 92, 1–14.Google Scholar
Craik, A. D. D. 1985 Wave Interactions and Fluid Flows. Cambridge University Press.
Craik, A. D. D. & Adam, J. A. 1979 ‘Explosive’ resonant wave interactions in a three-layer fluid flow. J. Fluid Mech. 92, 15–33.Google Scholar
Davidson, R. C. 1972 Methods in Nonlinear Plasma Theory. Academic.
Grimshaw, R. 1984 Wave action and wave-mean flow interaction, with application to stratified shear flows. Ann. Rev. Fluid Mech. 16, 11–44.Google Scholar
Kaup, D. J., Reiman, A. & Bers, A. 1979 Space-time evolution of nonlinear three-wave interactions. I. Interaction in a homogeneous medium. Rev. Mod. Phys. 51, 275–309.Google Scholar
Maslowe, S. A. 1973 Finite-amplitude Kelvin–Helmholtz billows. Boundary-Layer Met. 5, 43–52.Google Scholar
Maslowe, S. A. 1985 Shear flow instabilities and transition. In Hydrodynamic Instabilities and the Transition to Turbulence (ed. H. L. Swinney & J. P. Gollub), pp. 181–228. Springer.
Morland, L. C., Saffman, P. G. & Yuen, H. C. 1991 Waves generated by shear layer instabilities. Proc. R. Soc. Lond. A 433, 441–450.Google Scholar
Ostrovskii, L. A., Rybak, S. A. & Tsmring, L. Sh. 1986 Negative energy waves in hydrodynamics. Sov. Phys. Usp. 29, 1040–1052.Google Scholar
Romanova, N. N. & Shrira, V. I. 1988 Explosive generation of surface waves by the wind. Izv. Atmos. Ocean. Phys. 24, 528–535.Google Scholar
Simmons, W. F. 1969 A variational method for weak resonant wave interactions. Proc. R. Soc. Lond. A 309, 551–575.Google Scholar
Tsutahara, M. 1984 Resonant interactions of internal waves in a stratified shear flow. Phys. Fluids 27, 1942–1947.Google Scholar
Tsutahara, M. & Hashimoto, K. 1986 Three-wave resonant interactions and multiple resonances in two-layer and three-layer flows. Phys. Fluids 29, 2812–2818.Google Scholar
Zhang, J. 1991 Fourth-order Lagrangian of short waves riding on long waves. Phys. Fluids A 3, 3007–3013.Google Scholar