A Unified Shell model for Buoyancy-Driven Turbulence
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Abstract
We construct a unified shell model for stably stratified and convective turbulence. Shell model simulation of stably stratified flow in turbulent regime exhibit Bolgiano-Obukhbov (BO) scaling in which the kinetic energy spectrum varies as $k^{-11/5}$. However, simulation of convective turbulence shows Kolmogorov's spectrum. These results are consistent with the direct numerical simulations of Kumar {\em et al.} [Phys. Rev. E {\bf 90}, 023016 (2014)]. We also observe a dual scaling ($k^{-11/5}$ and $k^{-5/3}$) for a limited range of parameters in stably stratified flow.