Energy Spectrum and Flux of Buoyancy-Driven Turbulence

Abstract

Using direct numerical simulation we demonstrate that for isotropic stably-stratified flows follow Bolgiano-Obukhov scaling, i.e., the kinetic energy spectrum Eu(k) ∼ k−11/5, the entropy spectrum Eθ(k) ∼ k−7/5, and kinetic energy flux Πu(k) ∼ k−4/5. This is due to the conversion of kinetic energy to potential energy because of buoyancy. For Rayleigh Bénard convection, we argue that Πu(k) is a nondecreasing function of k due to the positive energy supply rate by buoyancy. Our numerical simulations show that the convection turbulence follows Kolmogorov-like scaling (Eu(k) ∼ k−5/3) with Kolmogorov's constant approximately 1.4.