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Heat transfer in rapidly rotating convection with heterogeneous thermal boundary conditions

Published online by Cambridge University Press:  05 September 2017

Jon E. Mound Open the ORCID record for Jon E. Mound [Opens in a new window]  and
Christopher J. Davies
Jon E. Mound*
Affiliation:
School of Earth and Environment, University of Leeds, Leeds LS2 9JT, UK
Christopher J. Davies
Affiliation:
School of Earth and Environment, University of Leeds, Leeds LS2 9JT, UK Institute of Geophysics and Planetary Physics, Scripps Institution of Oceanography, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0225, USA
*
†Email address for correspondence: j.e.mound@leeds.ac.uk
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Abstract

Convection in the metallic cores of terrestrial planets is likely to be subjected to lateral variations in heat flux through the outer boundary imposed by creeping flow in the overlying silicate mantles. Boundary anomalies can significantly influence global diagnostics of core convection when the Rayleigh number, $Ra$, is weakly supercritical; however, little is known about the strongly supercritical regime appropriate for planets. We perform numerical simulations of rapidly rotating convection in a spherical shell geometry and impose two patterns of boundary heat flow heterogeneity: a hemispherical $Y_{1}^{1}$ spherical harmonic pattern; and one derived from seismic tomography of the Earth’s lower mantle. We consider Ekman numbers $10^{-4}\leqslant E\leqslant 10^{-6}$, flux-based Rayleigh numbers up to ${\sim}800$ times critical, and a Prandtl number of unity. The amplitude of the lateral variation in heat flux is characterised by $q_{L}^{\ast }=0$, 2.3, 5.0, the peak-to-peak amplitude of the outer boundary heat flux divided by its mean. We find that the Nusselt number, $Nu$, can be increased by up to ${\sim}25\,\%$ relative to the equivalent homogeneous case due to boundary-induced correlations between the radial velocity and temperature anomalies near the top of the shell. The $Nu$ enhancement tends to become greater as the amplitude and length scale of the boundary heterogeneity are increased and as the system becomes more supercritical. This $Ra$ dependence can steepen the $Nu\propto Ra^{\unicode[STIX]{x1D6FE}}$ scaling in the rotationally dominated regime, with $\unicode[STIX]{x1D6FE}$ for our most extreme case approximately 20 % greater than the equivalent homogeneous scaling. Therefore, it may be important to consider boundary heterogeneity when extrapolating numerical results to planetary conditions.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Rotating flows
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Papers
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Journal of Fluid Mechanics , Volume 828 , 10 October 2017 , pp. 601 - 629
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© 2017 Cambridge University Press 

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