Heat transfer in rapidly rotating convection with heterogeneous thermal boundary conditions

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 Earth's lower mantle. We consider Ekman numbers 10 −4 E 10 −6 , flux-based Rayleigh numbers up to ∼ 800 times critical, and Prandtl number unity. The amplitude of the lateral variation in heat flux is characterised by q * L = 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 ∼ 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 ∝ Ra γ scaling in the rotationally dominated regime, with γ 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. Key words: Authors should not enter keywords on the manuscript, as these must be chosen by the author during the online submission process and will then be added during the typesetting process (see http://journals.cambridge.org/data/relatedlink/jfmkeywords.pdf for the full list)

Scaling Laws for Regional Stratification at the top of Earth’s Core

“…Grossmann and Lohse, 2000;Gastine et al, 2016;Aurnou and King, 2017;Schwaiger et al, 2019;Aubert, 2019). The goodness of our fits (figures 1 and 2) and previous analysis (Mound and Davies, 2017;Long et al, 2019) indicate that the IAC balance holds in the simulations we have considered here. The dynamic balance enters into the scaling for L (equation 10) by determining the small length-scale associated with convection.…”

“…King et al, 2013;Jones, 2015;Gastine et al, 2016;Aubert et al, 2017). For the turbulent rotating convection of our simulations we expect Inertial, Archimedean buoyancy, and Coriolis forces to be important and focus on this regime (characterised by the IAC balance), which holds in 34 of our previously presented simulations (Mound and Davies, 2017;Long et al, 2019).…”

“…where the flux Rayleigh number Ra F = Ra/E (Mound and Davies, 2017). Therefore, we expect that the thickness of the regional inversion lenses should scale as…”

Regional stratification at the top of Earth's core due to core–mantle boundary heat flux variations

“…The top of the core will also be strongly influenced by thermal heterogeneity in the lowermost mantle, which is much stronger than in the core (o{10 2 K}) and evolves much more slowly, such that the mantle imposes a laterally varying pattern of heat flux across the core-mantle boundary (CMB) 24 . Estimates of the lateral variations in CMB heat flux [25][26][27] are sufficiently large that significant regional variations in core dynamics are expected 16,[28][29][30][31] . Previous models 16,[32][33][34] have considered the interaction between CMB heterogeneity and stratification at the top of the core and the extent to which such heterogeneity can drive flows that penetrate and possibly disrupt a global stratified layer 24,35 .…”

Infinite family of universal profiles for heat current statistics in Fourier's law

“…The MFT equations lead to a variational problem for G(J), which can be written in terms of the optimal temperature and current fields as shown in Eq. (20). As a result, using the additivity principle [88] and taking into account the structure of the optimal temperature fields (25) and its relation with the optimal heat current (21), we arrive at the following expression for the current LDF…”