In this paper we present a unified shell model for stably stratified and convective turbulence. Numerical simulation of this model for stably stratified flow shows Bolgiano-Obukhbov scaling in which the kinetic energy spectrum varies as k-11/5. The shell model of convective turbulence yields Kolmogorov's spectrum. These results are consistent with the energy flux and energy feed due to buoyancy, and are in good agreement with direct numerical simulations of Kumar et al. [Phys. Rev. E 90, 023016 (2014)10.1103/PhysRevE.90.023016].
Kumar, A., & Verma, M. K. (2015). Shell model for buoyancy-driven turbulence. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 91(4). https://doi.org/10.1103/PhysRevE.91.043014