# Contrasting turbulence in stably stratified flows and thermal convection

## TL;DR

This paper compares stably stratified turbulence and turbulent thermal convection, highlighting differences in buoyancy effects, energy fluxes, and energy spectra, revealing distinct turbulence characteristics in stable versus unstable flows.

## Contribution

It provides a detailed contrast of turbulence properties in stable and unstable stratified flows, emphasizing the role of buoyancy and resulting energy spectra differences.

## Key findings

- SST has negative buoyancy feedback, leading to steep energy spectra (~k^{-11/5})
- Turbulent convection exhibits positive buoyancy, with energy spectra similar to hydrodynamic turbulence (~k^{-5/3})
- Distinct energy flux behaviors are characterized for stable and unstable stratified flows.

## Abstract

In this paper, the properties of stably stratified turbulence (SST) and turbulent thermal convection are contrasted. A key difference between these flows is the sign of the kinetic energy feed by buoyancy, $\mathcal{F}_B$. For SST, $\mathcal{F}_B < 0$ due to its stable nature; consequently, the kinetic energy flux $\Pi_u(k)$ decreases with wavenumber $k$ that leads to a steep kinetic energy spectrum, $E_u(k) \sim k^{-11/5}$. Turbulent convection is unstable, hence $\mathcal{F}_B > 0$ that leads to an increase of $\Pi_u(k)$ with $k$; this increase however is marginal due to relatively weak buoyancy, hence $E_u(k) \sim k^{-5/3}$, similar to that in hydrodynamic turbulence. This paper also describes the conserved fluxes for the above systems.