Does the thermal wind exist near the Earth's core boundary?

Temperature distribution in the Earth core determines many important processes such as the following: convective motion, magnetic field generation, matter exchange between the core and the mantle, and the thermal flux. This distribution depends on conditions in the core-mantle boundary and on the distribution of the thermal conductivity in the mantle. Seismic tomography shows that large horizontal temperature and compositional gradients exists at the core-mantle boundary. The simple assumption that these inhomogeneities are extended into the top of the core contradicts the common opinion that the horizontal temperature gradient (the thermal wind) wipes them out in a short time. However, this conclusion has been obtained without taking into account that the core volume is closed and the motion, if it is started, can lead to a small redistribution of composition that stops this motion.