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

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References

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