Scaling of mixed velocity-temperature derivative skewness in stationary homogeneous isotropic turbulence with a uniform mean scalar gradient

Transport equations for the mean squared scalar derivatives in stationary homogeneous isotropic turbulence with a uniform mean scalar gradient are derived from the transport equations for the second-order scalar derivative tensor. After some manipulation of the equations, it is shown that the large-scale forcing caused by the mean scalar gradient can be recast in the form R i S θ * P e λ θ − 1 ( S θ * is the non-dimensional mean scalar gradient, P e λ θ is the turbulent Péclet number, and R i ( i = 1 , 2 , 3 ) are the normalized mixed velocity-scalar derivatives). The effect of the large-scale forcing gradually disappears as P e λ θ becomes sufficiently large, implying a gradual approach toward a constant value of the mixed velocity-temperature derivative skewness with increasing P e λ θ . The trend of available data for the dependence of this mixed skewness, both with respect to the Reynolds number for a fixed Sc and with respect to Sc for a fixed Reynolds number, is consistent with the analysis.