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Non-geostrophic instabilities of an equilibrium baroclinic state

Published online by Cambridge University Press:  14 October 2013

Alexandre B. Pieri ,
F. S. Godeferd ,
C. Cambon  and
A. Salhi
Alexandre B. Pieri
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, École Centrale de Lyon, Université de Lyon, France
F. S. Godeferd*
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, École Centrale de Lyon, Université de Lyon, France
C. Cambon
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, École Centrale de Lyon, Université de Lyon, France
A. Salhi
Affiliation:
Département de Physique, Faculté des Sciences de Tunis, Université de Tunis El Manar, 1060 Tunis, Tunisia
*
†Email address for correspondence: Fabien.Godeferd@ec-lyon.fr
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Abstract

We consider non-geostrophic homogeneous baroclinic turbulence without solid boundaries, and we focus on its energetics and dynamics. The homogeneous turbulent flow is therefore submitted to both uniform vertical shear $S$ and stable vertical stratification, parametrized by the Brunt–Väisälä frequency $N$, and placed in a rotating frame with Coriolis frequency $f$. Direct numerical simulations show that the threshold of baroclinic instability growth depends mostly on two dimensionless numbers, the gradient Richardson number $\mathit{Ri}= {N}^{2} / {S}^{2} $ and the Rossby number $\mathit{Ro}= S/ f$, whereas linear theory predicts a threshold that depends only on $\mathit{Ri}$. At high Rossby numbers the nonlinear limit is found to be $\mathit{Ri}= 0. 2$, while in the limit of low $\mathit{Ro}$ the linear stability bound $\mathit{Ri}= 1$ is recovered. We also express the stability results in terms of background potential vorticity, which is an important quantity in baroclinic flows. We show that the linear symmetric instability occurs from the presence of negative background potential vorticity. The possibility of simultaneous existence of symmetric and baroclinic instabilities is also investigated. The dominance of symmetric instability over baroclinic instability for $\mathit{Ri}\ll 1$ is confirmed by our direct numerical simulations, and we provide an improved understanding of the dynamics of the flow by exploring the details of energy transfers for moderate Richardson numbers.

JFM classification

Geophysical and Geological Flows: Baroclinic flows Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 734 , 10 November 2013 , pp. 535 - 566
Copyright
©2013 Cambridge University Press 

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