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Large-scale vortices in rapidly rotating Rayleigh–Bénard convection

Published online by Cambridge University Press:  09 October 2014

Céline Guervilly ,
David W. Hughes  and
Chris A. Jones
Céline Guervilly*
Affiliation:
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
David W. Hughes
Affiliation:
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
Chris A. Jones
Affiliation:
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
*
†Email address for correspondence: [email protected]
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Abstract

Using numerical simulations of rapidly rotating Boussinesq convection in a Cartesian box, we study the formation of long-lived, large-scale, depth-invariant coherent structures. These structures, which consist of concentrated cyclones, grow to the horizontal scale of the box, with velocities significantly larger than the convective motions. We vary the rotation rate, the thermal driving and the aspect ratio in order to determine the domain of existence of these large-scale vortices (LSV). We find that two conditions are required for their formation. First, the Rayleigh number, a measure of the thermal driving, must be several times its value at the linear onset of convection; this corresponds to Reynolds numbers, based on the convective velocity and the box depth, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\gtrsim }100$. Second, the rotational constraint on the convective structures must be strong. This requires that the local Rossby number, based on the convective velocity and the horizontal convective scale, ${\lesssim }0.15$. Simulations in which certain wavenumbers are artificially suppressed in spectral space suggest that the LSV are produced by the interactions of small-scale, depth-dependent convective motions. The presence of LSV significantly reduces the efficiency of the convective heat transport.

JFM classification

Turbulent Flows: Rotating turbulence Turbulent Flows: Turbulent convection Vortex Flows: Vortex dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 758 , 10 November 2014 , pp. 407 - 435
Copyright
© 2014 Cambridge University Press 

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