# Velocity-vorticity correlation and turbulent diffusivity in buoyancy driven fluid dynamics

## TL;DR

This paper explores how the velocity-vorticity correlation integral can be used to describe turbulent diffusivity in buoyancy-driven flows, supported by numerical simulations of various convection and mixing phenomena.

## Contribution

It demonstrates that the velocity-vorticity correlation integral effectively characterizes turbulence in buoyancy-driven systems, linking invariant properties to turbulent diffusivity.

## Key findings

- Distributed chaos governed by the invariant explains Rayleigh-Bénard convection.
- The approach applies to stably stratified turbulence.
- It models Rayleigh-Taylor mixing at Prandtl number around 1.

## Abstract

The velocity-vorticity correlation integral (Chkhetiani invariant) is an invariant of a viscous Karman-Howarth equation. In the tree-dimensional space this invariant can naturally determine a turbulent diffusivity (viscosity). It is shown, using results of direct numerical simulations, that distributed chaos dominated by this integral can provide an adequate description of the turbulent Rayleigh-B\'{e}nard convection, stably stratified turbulence and Rayleigh-Taylor mixing at Prandtl number $Pr \sim 1$.