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Energetics of horizontal convection

  • Bishakhdatta Gayen (a1), Ross W. Griffiths (a1), Graham O. Hughes (a1) and Juan A. Saenz (a1)

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.

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Gregory, J. M. & Tailleux, R. 2011 Kinetic energy analysis of the response of the Atlantic meridional overturning circulation to CO2-forced climate change. Clim. Dyn. 37, 893914.
Hughes, G. O. & Griffiths, R. W. 2008 Horizontal convection. Annu. Rev. Fluid Mech. 40, 185208.
Hughes, G. O., Griffiths, R. W., Mullarney, J. C. & Peterson, W. H. 2007 A theoretical model for horizontal convection at high Rayleigh number. J. Fluid Mech. 581, 251276.
Hughes, G. O., Hogg, A. McC. & Griffiths, R. W. 2009 Available potential energy and irreversible mixing in the meridional overturning circulation. J. Phys. Oceanogr. 39, 31303146.
Mullarney, J. C., Griffiths, R. W. & Hughes, G. O. 2004 Convection driven by differential heating at a horizontal boundary. J. Fluid Mech. 516, 181209.
Paparella, F. & Young, W. R. 2002 Horizontal convection is non-turbulent. J. Fluid Mech. 466, 205214.
Rossby, H. T. 1965 On thermal convection driven by non-uniform heating from below: an experimental study. Deep Sea Res. 12, 916.
Rossby, H. T. 1998 Numerical experiments with a fluid heated non-uniformly from below. Tellus A 50, 242257.
Saenz, J. A., Hogg, A. McC., Hughes, G. O. & Griffiths, R. W. 2012 Mechanical power input from buoyancy and wind to the circulation in an ocean model. Geophys. Res. Lett. 39, L13605.
Scotti, A. & White, B. 2011 Is horizontal convection really “non-turbulent”? Geophys. Res. Lett. 38, L21609.
Stevens, R. J. A. M., Verzicco, R. & Lohse, D. 2010 Radial boundary layer structure and Nusselt number in Rayleigh–Bénard convection. J. Fluid Mech. 643, 495507.
Stewart, K. D., Hughes, G. O. & Griffiths, R. W. 2011 When do marginal seas and topographic sills modify the ocean density structure? J. Geophys. Res. 116, C08021.
Stewart, K. D., Hughes, G. O. & Griffiths, R. W. 2012 The role of turbulent mixing in an overturning circulation maintained by surface buoyancy forcing. J. Phys. Oceanogr. 42, 19071922.
Tailleux, R. 2009 On the energetics of stratified turbulent mixing, irreversible thermodynamics, Boussinesq models and the ocean heat engine controversy. J. Fluid Mech. 638, 339382.
Turner, J. S. 1986 Turbulent entrainment: the development of the entrainment assumption, and its application in geophysical flows. J. Fluid Mech. 173, 431471.
Winters, K. B., Lombard, P. N., Riley, J. J. & D’Asaro, E. A. 1995 Available potential energy and mixing in density-stratified fluids. J. Fluid Mech. 289, 115128.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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