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Geostrophic and chimney regimes in rotating horizontal convection with imposed heat flux

Published online by Cambridge University Press:  15 June 2017

Catherine A. Vreugdenhil Open the ORCID record for Catherine A. Vreugdenhil [Opens in a new window] ,
Ross W. Griffiths Open the ORCID record for Ross W. Griffiths [Opens in a new window]  and
Bishakhdatta Gayen Open the ORCID record for Bishakhdatta Gayen [Opens in a new window]
Catherine A. Vreugdenhil*
Affiliation:
Research School of Earth Sciences, Australian National University, Canberra, ACT 2601, Australia
Ross W. Griffiths
Affiliation:
Research School of Earth Sciences, Australian National University, Canberra, ACT 2601, Australia
Bishakhdatta Gayen
Affiliation:
Research School of Earth Sciences, Australian National University, Canberra, ACT 2601, Australia
*
†Email address for correspondence: Catherine.Vreugdenhil@anu.edu.au
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Abstract

Convection in a rotating rectangular basin with differential thermal forcing at one horizontal boundary is examined using laboratory experiments. The experiments have an imposed heat flux boundary condition, are at large values of the flux Rayleigh number ($Ra_{F}\sim O(10^{13}{-}10^{14})$ based on the box length $L$), use water with Prandtl number $Pr\approx 4$ and have a small depth to length aspect ratio. The results show the conditions for transition from non-rotating horizontal convection governed by an inertial–buoyancy balance in the thermal boundary layer, to circulation governed by geostrophic flow in the boundary layer. The geostrophic balance constrains mean flow and reduces the heat transport as Nusselt number $Nu\sim (Ra_{F}Ro)^{1/6}$, where $Ro=B^{1/2}/f^{3/2}L$ is the convective Rossby number, $B$ is the imposed buoyancy flux and $f$ is the Coriolis parameter. Thus flow in the geostrophic boundary layer regime is governed by the relative roles of horizontal convective accelerations and Coriolis accelerations, or buoyancy and rotation, in the boundary layer. Experimental evidence suggests that for more rapid rotation there is another transition to a regime in which the momentum budget is dominated by fluctuating vertical accelerations in a region of vortical plumes, which we refer to as a ‘chimney’ following related discussion of regions of deep convection in the ocean. Coupling of the chimney convection in the region of destabilising boundary flux to the diffusive boundary layer of horizontal convection in the region of stabilising boundary flux gives heat transport independent of rotation in this ‘inertial chimney’ regime, and the new scaling $Nu\sim Ra_{F}^{1/4}$. Scaling analysis predicts the transition conditions observed in the experiments, as well as a further ‘geostrophic chimney’ regime in which the vertical plumes are controlled by local geostrophy. When $Ro<10^{-1}$, the convection is also observed to produce a set of large basin-scale gyres at all depths in the time-averaged flow.

JFM classification

Geophysical and Geological Flows: Ocean circulation Geophysical and Geological Flows: Rotating flows Turbulent Flows: Turbulent convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 823 , 25 July 2017 , pp. 57 - 99
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© 2017 Cambridge University Press 

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Vreugdenhil et al. supplementary movie

Side view movie from Experiment 4 with dye tracer and showing only the heated half of the box (RaF = 6.5 z 1014, f = 0.4s-1, Ro = 5.6 z 10-3).

Download Vreugdenhil et al. supplementary movie(Video)
Video 22.4 MB

Vreugdenhil et al. supplementary movie

Side view movie from Experiment 6 with dye tracer and showing only the heated half of the box (RaF = 6.8 z 1014, f = 1.6s-1, Ro = 7.1 z 10-4).

Download Vreugdenhil et al. supplementary movie(Video)
Video 29.7 MB