Hostname: page-component-7f64f4797f-d87pz Total loading time: 0 Render date: 2025-11-04T13:40:00.581Z Has data issue: false hasContentIssue false
  • English
  • Français

On three-dimensional internal gravity wave beams and induced large-scale mean flows

Published online by Cambridge University Press:  25 March 2015

T. Kataoka  and
T. R. Akylas
T. Kataoka
Affiliation:
Department of Mechanical Engineering, Graduate School of Engineering, Kobe University, Rokkodai, Nada, Kobe 657-8501, Japan
T. R. Akylas*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: trakylas@mit.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

The three-dimensional propagation of internal gravity wave beams in a uniformly stratified Boussinesq fluid is discussed, assuming that variations in the along-beam and transverse directions are of long length scale relative to the beam width. This situation applies, for instance, to the far-field behaviour of a wave beam generated by a horizontal line source with weak transverse dependence. In contrast to the two-dimensional case of purely along-beam variations, where nonlinear effects are minor even for beams of finite amplitude, three-dimensional nonlinear interactions trigger the transfer of energy to a circulating horizontal time-mean flow. This resonant beam–mean-flow coupling is analysed, and a system of two evolution equations is derived for the propagation of a small-amplitude beam along with the induced mean flow. This model explains the salient features of the experimental observations of Bordes et al. (Phys. Fluids, vol. 24, 2012, 086602).

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Internal waves

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 769 , 25 April 2015 , pp. 621 - 634
Copyright
© 2015 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.)

Article purchase

Temporarily unavailable

References

Bordes, G., Venaille, A., Joubaud, S., Odier, P. & Dauxois, T. 2012 Experimental observation of a strong mean flow induced by internal gravity waves. Phys. Fluids 24, 086602.Google Scholar
Gostiaux, L., Didelle, H., Mercier, S. & Dauxois, T. 2007 A novel internal waves generator. Exp. Fluids 42, 123–130.Google Scholar
Grisouard, N. & Bühler, O. 2012 Forcing of oceanic mean flows by dissipating internal tides. J. Fluid Mech. 708, 250–278.CrossRefGoogle Scholar
Grisouard, N., Leclair, M., Gostiaux, L. & Staquet, C. 2013 Large scale energy transfer from an internal gravity wave reflecting on a simple slope. Proc. IUTAM 8, 119–128.CrossRefGoogle Scholar
Karimi, H. H. & Akylas, T. R. 2014 Parametric subharmonic instability of internal waves: locally confined beams versus monochromatic wavetrains. J. Fluid Mech. 757, 381–402.Google Scholar
Kataoka, T. & Akylas, T. R. 2013 Stability of internal gravity wave beams to three-dimensional modulations. J. Fluid Mech. 736, 67–90.Google Scholar
Koudella, C. R. & Staquet, C. 2006 Instability mechanisms of a two-dimensional progressive internal gravity wave. J. Fluid Mech. 548, 165–196.Google Scholar
Lighthill, M. J. 1978 Waves in Fluids. Cambridge University Press.Google Scholar
Lighthill, M. J. 1996 Internal waves and related initial-value problems. Dyn. Atmos. Oceans 23, 3–17.CrossRefGoogle Scholar
McEwan, A. D. 1973 Interactions between internal gravity waves and their traumatic effect on a continuous stratification. Boundary-Layer Meteorol. 5, 159–175.Google Scholar
Mercier, M. J., Martinand, D., Mathur, M., Gostiaux, L., Peacock, T. & Dauxois, T. 2010 New wave generation. J. Fluid Mech. 657, 308–334.CrossRefGoogle 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 fluid. J. Fluid Mech. 28, 1–16.Google Scholar
Staquet, C. & Sommeria, J. 2002 Internal gravity waves: from instabilities to turbulence. Annu. Rev. Fluid Mech. 34, 559–593.Google Scholar
Tabaei, A. & Akylas, T. R. 2003 Nonlinear internal gravity wave beams. J. Fluid Mech. 482, 141–161.CrossRefGoogle Scholar
Tabaei, A. & Akylas, T. R. 2007 Resonant long–short wave interactions in an unbounded rotating stratified fluid. Stud. Appl. Maths 119, 271–296.Google Scholar
Thomas, N. H. & Stevenson, T. N. 1972 A similarity solution for viscous internal waves. J. Fluid Mech. 54, 495–506.CrossRefGoogle Scholar