Energy spectrum of Buoyancy-driven Flows

Abstract

Using high-resolution direct numerical simulation and arguments based on the kinetic energy flux ${\Pi }_u$, we demonstrate that for stably stratified flows, the kinetic energy spectrum $E_u(k)\sim k^{-11/5}$, the entropy spectrum $E_{\theta }(k)\sim k^{-7/5}$, and ${\Pi }_u(k)\sim k^{-4/5}$ (Bolgiano-Obukhov scaling). This scaling is due to the depletion of kinetic energy because of buoyancy. For weaker buoyancy in stratified flows, $E_u(k)$ follows Kolmgorov's spectrum with a constant energy flux. We also argue that for Rayleigh Bénard convection, the Bolgiano-Obukhov scaling will not hold for the bulk flow due to the positive energy supply by buoyancy and non-decreasing ${\Pi }_u(k)$.

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