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

TL;DR

This paper investigates how heat transport scaling in internally heated turbulent convection transitions from boundary-limited to mixing-length behavior as heating and cooling rates become more balanced, using numerical simulations at Prandtl number one.

Contribution

It demonstrates the transition in heat transport scaling from boundary-limited to mixing-length regimes based on heating and cooling asymmetry in simulations.

Findings

Scaling exponent varies with heating-cooling balance.

Transition from boundary-limited to mixing-length scaling observed.

Numerical simulations at Prandtl number one support the findings.

Abstract

Heat transport in turbulent thermal convection increases with the 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 is slower than the mixing-length (or `ultimate') scaling. In configurations driven by either thermal boundary conditions or internal heating, thermal boundary layers instead lead to a boundary-limited (or `classical') scaling. With net-zero internal heating and cooling in different regions, mixing-length scaling can occur because heat need not cross a boundary. We report numerical simulations in which heating and cooling are unequal, as in various natural systems, at a Prandtl number of unity. 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.