  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 $Pr \sim 1$.
