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Sensitivity of rapidly rotating Rayleigh-Bénard convection to Ekman pumping

Meredith Plumley1,*, Keith Julien1, Philippe Marti1,2, and Stephan Stellmach3

  • 1Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309, USA
  • 2Institute of Geophysics, ETH Zurich, Zurich 8092, Switzerland
  • 3Institut für Geophysik, Westfälische Wilhelms-Universität, D-48149 Münster, Germany

  • *Corresponding author: meredith.plumley@colorado.edu
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Phys. Rev. Fluids 2, 094801 – Published 6 September, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.094801

Abstract

The dependence of the heat transfer, as measured by the nondimensional Nusselt number Nu, on Ekman pumping for rapidly rotating Rayleigh-Bénard convection in an infinite plane layer is examined for fluids with Prandtl number Pr=1. A joint effort utilizing simulations from the composite non-hydrostatic quasi-geostrophic model and direct numerical simulations (DNS) of the incompressible fluid equations has mapped a wide range of the Rayleigh number Ra-Ekman number E parameter space within the geostrophic regime of rotating convection. Corroboration of the Nu−Ra relation at E=10−7 from both methods along with higher E covered by DNS and lower E by the asymptotic model allows for this extensive range of the heat transfer results. For stress-free boundaries, the relation Nu−1∝(RaE4/3)α has the dissipation-free scaling of α=3/2 for all E≤10−7. This is directly related to a geostrophic turbulent interior that throttles the heat transport supplied to the thermal boundary layers. For no-slip boundaries, the existence of ageostrophic viscous boundary layers and their associated Ekman pumping yields a more complex two-dimensional surface in Nu(E,Ra) parameter space. For E<10−7 results suggest that the surface can be expressed as Nu−1∝[1+P(E)](RaE4/3)3/2 indicating the dissipation-free scaling law is enhanced by Ekman pumping by the multiplicative prefactor [1+P(E)] where P(E)≈5.97E1/8. It follows for E<10−7 that the geostrophic turbulent interior remains the flux bottleneck in rapidly rotating Rayleigh-Bénard convection. For E∼10−7, where DNS and asymptotic simulations agree quantitatively, it is found that the effects of Ekman pumping are sufficiently strong to influence the heat transport with diminished exponent α≈1.2 and Nu−1∝(RaE4/3)1.2.

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Phys. Rev. Fluids 2, 094801– Published 6 September, 2017
  • Received 14 April 2017
Article part of CHORUS

©2017 American Physical Society

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