Transition between Boundary-Limited Scaling and Mixing-Length Scaling of Turbulent Transport in Internally Heated Convection

Heat transport in turbulent thermal convection increases with thermal forcing, but in almost all studies the rate of this increase is slower than it would be if transport became independent of the molecular diffusivities-the heat transport scaling exponent is smaller than the mixing-length (or "ultimate") value of 1/2. This is due to thermal boundary layers that throttle heat transport in configurations driven either by thermal boundary conditions or by internal heating, giving a scaling exponent close to the boundary-limited (or "classical") value of 1/3. With net-zero internal heating and cooling in different regions, the larger mixing-length exponent can be attained because heat need not cross a boundary. We report numerical simulations in which heating and cooling are unequal. As heating and cooling rates are made closer, the scaling exponent of heat transport varies from its boundary-limited value to its mixing-length value.