Rigorous bounds on the heat transport of rotating convection with Ekman pumping
B. Pachev, J. P. Whitehead, G. Fantuzzi, I. Grooms
Source abstract
We establish rigorous upper bounds on the time-averaged heat transport for a model of rotating Rayleigh-Bénard convection between no-slip boundaries at infinite Prandtl numbers and with Ekman pumping. The analysis is based on the asymptotically reduced equations derived for rotationally constrained dynamics with no-slip boundaries, and hence, includes a lower order correction that accounts for the Ekman layer and corresponding Ekman pumping into the bulk. Using the auxiliary functional method, we find that, to leading order, the temporally averaged heat transport is bounded above as a function of the Rayleigh and Ekman numbers Ra and Ek according to Nu ≤ 0.3704Ra2Ek2. Dependent on the relative values of the thermal forcing represented by Ra and the effects of rotation represented by Ek, this bound is both an improvement on earlier rigorous upper bounds and provides a partial explanation of recent numerical and experimental results that were consistent yet surprising relative to the previously derived upper bound of Nu ≲ Ra3Ek4.
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