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On the genesis of quasi-steady vortices in a rotating turbulent flow

Published online by Cambridge University Press:  21 April 2006

Mathieu Mory  and
Philippe Caperan
Mathieu Mory
Affiliation:
Institut de Mécanique de Grenoble, Domaine Universitaire, BP 68, 38402 Saint Martin d'Hères Cédex, France
Philippe Caperan
Affiliation:
Institut de Mécanique de Grenoble, Domaine Universitaire, BP 68, 38402 Saint Martin d'Hères Cédex, France
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Abstract

Turbulent flows subjected to rotation display vortices parallel to the rotation axis and exhibiting a long timescale compared to the turbulent turnover time and the rotation period. A similar flow pattern is observed arising from the thermal instability in a rotating fluid. We demonstrate the analogy between turbulence and thermal convection in a rotating fluid. A basic quasi-geostrophic turbulent flow is considered which is forced at the bottom of the layer by a stochastic component of velocity parallel to the rotation axis. The turbulent basic state has no mean flow and the gradient along the rotation axis of the turbulent kinetic energy −∂z〈ω2〉 is analogous to the mean temperature profile in thermal convection. The linear perturbation equations of this basic turbulent state are given, where the thermal diffusion equation is replaced by the turbulent kinetic energy equation. Using a simple closure of this equation the model demonstrates the occurrence of an instability when the Reynolds number exceeds a critical value. Marginal stability curves are deduced by numerical integration of the perturbation equations. The results show order-of-magnitude agreement with laboratory experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 185 , December 1987 , pp. 121 - 136
Copyright
© 1987 Cambridge University Press

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