Energy Spectrum of Buoyancy-Driven Turbulence

Abhishek Kumar; Anando G. Chatterjee; Mahendra K. Verma

doi:10.1103/PhysRevE.90.023016

paper

Energy Spectrum of Buoyancy-Driven Turbulence

arXiv:1406.5359 · doi:10.1103/PhysRevE.90.023016

Abstract

Using high-resolution direct numerical simulation and arguments based on the kinetic energy flux $Π_{u}$ , we demonstrate that for stably stratified flows, the kinetic energy spectrum $E_{u} (k) \sim k^{- 11/5}$ , the entropy spectrum $E_{θ} (k) \sim k^{- 7/5}$ , and $Π_{u} (k) \sim k^{- 4/5}$ , consistent with the Bolgiano-Obukhov scaling. This scaling arises due to the conversion of kinetic energy to the potential energy by buoyancy. For weaker buoyancy, this conversion is weak, hence $E_{u} (k)$ follows Kolmogorov's spectrum with a constant energy flux. For Rayleigh Bénard convection, we show that the energy supply rate by buoyancy is positive, which leads to an increasing $Π_{u} (k)$ with $k$ , thus ruling out Bolgiano-Obukhov scaling for the convective turbulence. Our numerical results show that convective turbulence for unit Prandt number exhibits a constant $Π_{u} (k)$ and $E_{u} (k) \sim k^{- 5/3}$ for a narrow band of wavenumbers.

arXiv commentarXiv admin note: text overlap with arXiv:1404.2148

Energy Spectrum of Buoyancy-Driven Turbulence

Abstract

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