a1 Department of Earth and Planetary Science, University of California, Berkeley, CA 94720-4767, USA
a2 Institut für Geophysik, Westfälische Wilhelms-Universität Münster, Arbeitsgruppe Geodynamik, Corrensstraße 24, 48149 Münster, Germany
a3 Department of Earth and Space Sciences, University of California, Los Angeles, CA 90095-1567, USA
Turbulent, rapidly rotating convection has been of interest for decades, yet there exists no generally accepted scaling law for heat transfer behaviour in this system. Here, we develop an exact scaling law for heat transfer by geostrophic convection, , by considering the stability of the thermal boundary layers, where , and are the Nusselt, Rayleigh and Ekman numbers, respectively, and is the critical Rayleigh number for the onset of convection. Furthermore, we use the scaling behaviour of the thermal and Ekman boundary layer thicknesses to quantify the necessary conditions for geostrophic convection: . Interestingly, the predictions of both heat flux and regime transition do not depend on the total height of the fluid layer. We test these scaling arguments with data from laboratory and numerical experiments. Adequate agreement is found between theory and experiment, although there is a paucity of convection data for low .
(Received February 02 2011)
(Reviewed November 02 2011)
(Accepted November 05 2011)