Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-19T13:04:00.721Z Has data issue: false hasContentIssue false
  • English
  • Français

Over-reflection of internal-inertial waves from the mixed layer

Published online by Cambridge University Press:  20 April 2006

M. Kamachi  and
R. Grimshaw
M. Kamachi
Affiliation:
Research Institute for Applied Mechanics, Kyushu University 87, Kasuga-city, Fukuoka, 816, Japan
R. Grimshaw
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria 3052, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

Near-inertial oscillations associated with downward energy propagation are commonly observed in the upper ocean. Stern (1977) has suggested that these observations may be internal-inertial waves over-reflected from the shear zone at the base of the mixed layer. In this paper we develop a criterion for over-reflection as a function of wavenumber and frequency for a class of shear flows in the mixed layer. By examining the vertical profile of the vertical wave action flux we demonstrate that the source of the over-reflection is the shear at the base of the mixed layer, which is maintained by the wind-induced turbulent Reynolds stress, here parametrized as a body force. The relationship between over-reflection and the wave-induced Lagrangian-mean flow is determined. We also determine a criterion for unstable waves, and show that these are contiguous in wavenumber-frequency space with points of resonant over-reflection. However, the growth rates of these unstable waves are quite small, and in practice unstable waves will be indistinguishable from waves generated by over-reflection.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 141 , April 1984 , pp. 179 - 196
Copyright
© 1984 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

Acheson, D. J. 1976 On over-reflexion. J. Fluid Mech. 77, 433–472.Google Scholar
Andrews, D. G. & McIntyre, M. E. 1978a An exact theory of nonlinear waves on a Lagrangianmean flow. J. Fluid Mech. 89, 609–646.Google Scholar
Andrews, D. G. & McIntyre, M. E. 1978b On wave-action and its relatives. J. Fluid Mech. 89, 647–664.Google Scholar
Fu, L.-L. 1981 Observations and models of inertial waves in the deep ocean. Rev. Geophys. Space Phys. 19, 141–170.Google Scholar
Kroll, J. 1975 The propagation of wind-generated inertial oscillations from the surface into the deep ocean. J. Mar. Res. 33, 15–51.Google Scholar
Leaman, K. & Sanford, T. 1975 Vertical energy propagation of inertial waves. J. Geophys. Res. 80, 1975–1978.Google Scholar
Lindzen, R. S. & Rosenthal, A. J. 1976 On the instability of Helmholtz velocity profiles in stably stratified fluids when a lower boundary is present. J. Geophys. Res. 81, 1561–1571.Google Scholar
McIntyre, M. E. & Weissman, M. A. 1978 On radiating instabilities and resonant overreflection. J. Atmos. Sci. 35, 1190–1196.Google Scholar
Mollo-Christensen, E. 1977 Impingement of internal waves from below onto a moving mixed surface layer. J. Phys. Oceanogr. 7, 684–690.Google Scholar
Pollard, R. T. 1970 On the generation by winds of inertial waves in the ocean. Deep-Sea Res. 17, 795–812.Google Scholar
Pollard, R. T. & Millard, R. C. 1970 Comparison between observed and simulated wind-generated inertial oscillations. Deep-Sea Res. 17, 813–821.Google Scholar
Rossby, H. T. & Sanford, T. 1976 A study of time dependent currents observed in the velocity profiles through the main thermocline. J. Phys. Oceanogr. 6, 766–774.Google Scholar
Stern, M. E. 1977 Interaction of inertia-gravity waves with the wind. J. Mar. Res. 35, 479–498.Google Scholar