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 applying the limit at small separations to the generalized form of Yaglom's equation in two types of flows, those dominated mainly by a decay of energy in the streamwise direction and those which are forced, through a continuous injection of energy at large scales. In grid turbulence, the imbalance between the production of ∈_θ due to stretching of the temperature field and the destruction of ∈_θ by the thermal diffusivity is governed by the streamwise advection of ∈_θ by the mean velocity. This imbalance is intrinsically different from that in stationary forced periodic box turbulence (or SFPBT), which is virtually negligible. In essence, the different types of imbalance represent different constraints imposed by the large-scale motion on the relation between the so-called mixed velocity-temperature derivative skewness S_T and the scalar enstrophy destruction coefficient G_θ in different flows, thus resulting in non-universal approaches of S_T towards a constant value as Re_λ increases. The data for S_T collected in grid turbulence and in SFPBT indicate that the magnitude of S,sub>T is bounded, this limit being close to 0.5.