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The breaking of transient inertio-gravity waves in a shear flow using the Gaussian beam approximation

Published online by Cambridge University Press:  27 October 2014

C. Rodas  and
M. Pulido
C. Rodas
Affiliation:
Physics Department, FACENA, Universidad Nacional del Nordeste, Corrientes, Argentina
M. Pulido*
Affiliation:
Physics Department, FACENA, Universidad Nacional del Nordeste, Corrientes, Argentina IMIT, UMI-IFAECI/CNRS, CONICET, Argentina
*
†Email address for correspondence: pulido@unne.edu.ar
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Abstract

The propagation of transient inertio-gravity waves in a shear flow is examined using the Gaussian beam formulation. This formulation assumes Gaussian wavepackets in the spectral space and uses a second-order Taylor expansion of the phase of the wave field. In this sense, the Gaussian beam formulation is also an asymptotic approximation like spatial ray tracing; however, the first one is free of the singularities found in spatial ray tracing at caustics. Therefore, the Gaussian beam formulation permits the examination of the evolution of transient inertio-gravity wavepackets from the initial time up to the destabilization of the flow close to the critical levels. We show that the transience favours the development of the dynamical instability relative to the convective instability. In particular, there is a well-defined threshold for which small initial amplitude transient inertio-gravity waves never reach the convective instability criterion. This threshold does not exist for steady-state inertio-gravity waves for which the wave amplitude increases indefinitely towards the critical level. The Gaussian beam formulation is shown to be a powerful tool to treat analytically several aspects of inertio-gravity waves in simple shear flows. In more realistic shear flows, its numerical implementation is readily available and the required numerical calculations have a low computational cost.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Waves in rotating fluids
Type
Papers
Information
Journal of Fluid Mechanics , Volume 759 , 25 November 2014 , pp. 676 - 700
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© 2014 Cambridge University Press 

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