Mechanical energy budget of turbulent rayleigh-benard convection - Gayen,B; Hughes,GO; Griffiths,RW (2015)
Turbulent Rayleigh-Bénard convection (RBC) is examined in terms of its mechanical energy budget. Three-dimensional large-eddy and direct numerical simulations are conducted at moderately large Rayleigh numbers. An expanded view of the mechanical energy pathways for RBC convection is developed for the the first time by recognising that mechanical energy includes gravitational potential energy and that the available component of this potential energy (APE) is the energy source for convection. The partitioning of energy pathways between large and small scales of motion is also analysed based on their corresponding temporal scales. The relative magnitudes of different pathways change significantly over the range of Rayleigh numbers Ra ∼ 107 - 1013. At Ra < 107 small-scale turbulent motions are energized directly from APE via turbulent buoyancy flux while kinetic energy is dissipated at comparable rates by both the large- and small-scale motions. In contrast, at Ra ≥ 1010 most of the APE goes into kinetic energy of the large-scale flow, and the large scales undergo shear instabilities that sustain small-scale turbulence. At large Ra one half of the total APE supply goes to viscous dissipation of kinetic energy and the other half to mixing of the thermal field. Therefore, mixing efficiency approaches 50% at large Ra, as also predicted by a scaling analysis. At large Rayleigh number the viscous dissipation is largely in the interior, while the irreversible mixing is largely confined to the unstable boundary layers. The inclusion of the mechanical energy in the budget provides new information on the roles of different length scales and on the mechanics of the interior and boundary layer.