Available potential energy in Rayleigh-Bénard convection

Abstract

The energy budget for thermally-equilibrated Rayleigh-Bénard convection is developed theoretically, with explicit consideration of the role of available potential energy. The analysis shows that about half of the available potential energy generated by the thermal forcing is dissipated viscously by turbulence at high Rayleigh number. The remainder is consumed by diffusion acting to homogenise the temperature field. The results of direct numerical simulations of convection at Rayleigh numbers ranging from 108 to 1013 are also presented in support of this analysis. An important conclusion is that Rayleigh-Bénard convection may be viewed as a highly efficient mechanism of turbulent mixing in a stratified fluid. Show more