On the differential torque exerted on double concentric boundaries by in-between thermal convection*

The modern seismic tomography measurements have elucidated that, lubricated by the liquid outer-core, the solid inner-core rotates slightly faster than the rest solid parts, the mantle and crust. The fluid motion in the outer-core, which is still veiled for us, possibly asymmetric with respect to east/westward circulations via the Coriolis effect, so that outer-core thermal convection may propagate to pro/retrograde directions, which was pointed out by Kimura et al [Phys. Fluids 23 074101 (2011)]. Here, we revisit a speculation on whether thermal convection induced between double concentric axisymmetric boundaries could allow them to permanently rotate with a difference in rotation rate. We consider a simple system of double concentric cylindrical boundaries freely rotating around their axis and Boussinesq fluid confined between them, which are initially co-rotating at an identical rotation rate. We argue a possibility that thermal convection generated with an increase of the difference in temperature of the boundaries produce a small difference in magnitude of the net tangential stress on the boundaries.