Boundedness of the mixed velocity-temperature derivative skewness in homogeneous isotropic turbulence

The transport equation for the mean scalar dissipation rate ∈_θ is derived by applyingthe limit at small separations to the generalized form of Yaglom's equation in twotypes of flows, those dominated mainly by a decay of energy in the streamwisedirection and those which are forced, through a continuous injection of energy atlarge scales. In grid turbulence, the imbalance between the production of ∈_θ dueto stretching of the temperature field and the destruction of ∈_θ by the thermaldiffusivity is governed by the streamwise advection of ∈_θ by the mean velocity.This imbalance is intrinsically different from that in stationary forced periodic boxturbulence (or SFPBT), which is virtually negligible. In essence, the different typesof imbalance represent different constraints imposed by the large-scale motion on therelation between the so-called mixed velocity-temperature derivative skewness S_Tand the scalar enstrophy destruction coefficient G_θ in different flows, thus resultingin non-universal approaches of S_T towards a constant value as Re_Λ increases. Thedata for S_T collected in grid turbulence and in SFPBT indicate that the magnitudeof S_T is bounded, this limit being close to 0.5.