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 $Pr \sim 1$.
Categories: physics.flu-dyn