A Shell Model for Buoyancy-Driven Turbulence

TL;DR

This paper introduces a unified shell model for buoyancy-driven turbulence, capturing different scaling behaviors in stratified and convective flows, and aligns well with numerical simulations.

Contribution

It presents a novel shell model that unifies the description of stratified and convective turbulence, reproducing key spectral scalings.

Findings

Bolgiano-Obukhov scaling with $k^{-11/5}$ in stratified turbulence

Dual scaling observed under certain parameters

Kolmogorov spectrum in convective turbulence

Abstract

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 $k^{-11/5}$. We also observe a dual scaling ($k^{-11/5}$ and $k^{-5/3}$) for a limited range of parameters. 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 {\em et al.} [Phys. Rev. E {\bf 90}, 023016 (2014)].