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Stability of internal gravity wave beams to three-dimensional modulations

Published online by Cambridge University Press:  01 November 2013

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: [email protected]
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Abstract

The linear stability of uniform, plane internal wave beams with locally confined spatial profile, in a stratified fluid of constant buoyancy frequency, is discussed. The associated eigenvalue problem is solved asymptotically, assuming perturbations of long wavelength relative to the beam width. In this limit, instability is found only for oblique disturbances which vary in the along-beam and the horizontal transverse directions. The mechanism of instability is a first-harmonic–mean resonant interaction between the underlying wave beam and three-dimensional perturbations that comprise a time-harmonic component, with the beam frequency, and a mean flow. Progressive beams which transport energy in one direction, in particular, are unstable if the beam steepness exceeds a certain threshold value, whereas purely standing beams are unstable even at infinitesimal steepness. A distinguishing feature of this three-dimensional modulational instability is the generation of circulating horizontal mean flows at large distances from the vicinity of the beam.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Instability: Instability Geophysical and Geological Flows: Internal waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 736 , 10 December 2013 , pp. 67 - 90
Copyright
©2013 Cambridge University Press 

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