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Energetics of horizontal convection

Published online by Cambridge University Press:  28 January 2013

Bishakhdatta Gayen ,
Ross W. Griffiths ,
Graham O. Hughes  and
Juan A. Saenz
Bishakhdatta Gayen
Affiliation:
Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia
Ross W. Griffiths*
Affiliation:
Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia
Graham O. Hughes
Affiliation:
Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia
Juan A. Saenz
Affiliation:
Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia
*
†Email address for correspondence: Ross.Griffiths@anu.edu.au
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Abstract

Three-dimensional direct numerical simulation of horizontal convection is reported for a large Rayleigh number, $\mathit{Ra}\sim O(1{0}^{12} )$, and boundary conditions that allow comparison with previous laboratory experiments. The convection is forced by heating over half of the horizontal base of a long channel and cooling over the other half of the base. The solutions are consistent with the experiments, including small-scale streamwise roll instability developing into a convectively mixed layer within the bottom thermal boundary layer, and a turbulent endwall plume. The mechanical energy budget is shown to be dominated by conversions of available potential energy to kinetic energy by buoyancy flux in the plume and the reverse in the interior of the circulation. These local conversions are three orders of magnitude greater than the total rate of viscous dissipation. The total irreversible mixing is exactly equal to the generation of available potential energy by buoyancy forcing, and one order of magnitude larger than the viscous dissipation. This confirms that dissipation rate is not an indicator of the strength of the circulation and explains why horizontal convection is more energetic than might be expected.

JFM classification

Convection: Buoyancy-driven instability Convection: Convection Geophysical and Geological Flows: Ocean circulation
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 716 , 10 February 2013 , R10
Copyright
©2013 Cambridge University Press

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Gayen et al. supplementary movie

Horizontal velocity field on the spanwise (y) mid-plane for the simulations at Ra = 5.86 x 1011, Pr = 5, and A = 0.16 (grid resolution 513 x 128 x 257 in x, y and z).

Download Gayen et al. supplementary movie(Video)
Video 9.6 MB

Gayen et al. supplementary movie

Vertical velocity field on the spanwise mid-plane for the simulations at Ra = 5.86 x 1011, Pr = 5, and A = 0.16 (grid resolution 513 x 128 x 257 in x, y and z).

Download Gayen et al. supplementary movie(Video)
Video 9.6 MB

Gayen et al. supplementary movie

Temperature field on the spanwise mid-plane for the simulations at Ra = 5.86 x 1011, Pr = 5, and A = 0.16 (grid resolution 513 x 128 x 257 in x, y and z).

Download Gayen et al. supplementary movie(Video)
Video 4.8 MB