Heat flux and shear rate in turbulent convection

One interesting feature of hard turbulence, a scaling regime in turbulent convection, is the presence of a large-scale mean circulating flow. Its effect on heat flux was studied by Shraiman and Siggia [Phys. Rev. A 42, 3650 (1990)], who approximated it as a shear flow near the boundaries. A constant shear rate was considered, which, in effect, assumes that heat is carried mainly by the mean flow. Experiments indicate, however, that a significant portion of heat is carried by the thermal plumes. In this paper, an analysis for a position-dependent shear rate is presented. The relation between the heat flux and the shear rate is found to depend crucially on the shape of the temperature profile. For the general profile that remains the same throughout a range of Rayleigh numbers, the relation is different from the previous result and agrees better with some recent experimental observations.