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Barotropic instability of a time-dependent parallel flow

Published online by Cambridge University Press:  05 July 2021

Timour Radko Open the ORCID record for Timour Radko [Opens in a new window]
Timour Radko*
Affiliation:
Department of Oceanography, Naval Postgraduate School, Monterey, CA93943, USA
*
† Email address for correspondence: tradko@nps.edu
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Abstract

This study examines the long-wavelength instabilities of an inviscid parallel time-dependent current on the beta-plane. The basic flow is represented by the Kolmogorov pattern, the amplitude of which is modulated in time. Particular attention is given to the regime in which the corresponding steady flows are stable according to the Rayleigh–Kuo criterion. It is shown that the presence of a fluctuating component, regardless of how weak it may be, always renders the basic current linearly unstable. The destabilization is attributed to the resonant forcing of large-scale Rossby waves. The analysis is based on the asymptotic multiscale model, which is validated by numerical simulations. Since most geophysical flows are inherently time-dependent, the associated shear instabilities could represent a significant and ubiquitous source of barotropic turbulence.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Instability: Instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 922 , 10 September 2021 , A11
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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