Completing the Mechanical Energy Pathways in Turbulent Rayleigh-Bénard Convection

A new, more complete view of the mechanical energy budget for Rayleigh-Bénard convection is developed and examined using three-dimensional numerical simulations at large Rayleigh numbers and Prandtl number of 1. The driving role of available potential energy is highlighted. The relative magnitudes of different energy conversions or pathways change significantly over the range of Rayleigh numbers Ra ~ 10(7)-10(13). At Ra < 10(7) small-scale turbulent motions are energized directly from available potential energy via turbulent buoyancy flux and kinetic energy is dissipated at comparable rates by both the large- and small-scale motions. In contrast, at Ra ≥ 10(10) most of the available potential energy goes into kinetic energy of the large-scale flow, which undergoes shear instabilities that sustain small-scale turbulence. The irreversible mixing is largely confined to the unstable boundary layer, its rate exactly equal to the generation of available potential energy by the boundary fluxes, and mixing efficiency is 50%