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Boundedness of the mixed velocity-temperature derivative skewness in homogeneous isotropic turbulence
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The transport equation for the mean scalar dissipation rate 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 due to stretching of the temperature field and the destruction of by the thermal diffusivity is governed by the streamwise advection of 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 ST and the scalar enstrophy destruction coefficient G
θ in different flows, thus resulting in non-universal approaches of ST towards a constant value as Re
λ increases. The data for ST collected in grid turbulence and in SFPBT indicate that the magnitude of ST is bounded, this limit being close to 0.5.
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