Uniform mean scalar gradient in grid turbulence: Asymptotic probability distribution of a passive scalar

An asymptotic self-similar solution is obtained for the one-point probability density function (pdf) equation, of a passive scalar with uniform mean gradient in incompressible homogeneous turbulence. It is argued that the same solution should be a valid approximation when turbulence is generated in a high-quality wind tunnel. The asymptotic pdf shape is a unique function of the conditional expectation of the normalized scalar dissipation rate. The mean scalar gradient modifies the scalar pdf shape only if the conditional expected velocity component in the direction of the mean gradient is a nonlinear function of scalar fluctuation value. Experimental data from wind tunnel studies are consistent with the sign and scale of the changes produced by these nonlinearities.