Predictions of small-scale statistics for a passive scalar in turbulent mixing

This Letter presents some quantitative predictions for the small-scale statistics for a passive scalar mixed in a fully turbulent flow. Our method uses an equation [S. Vaienti et al. Physica (Amsterdam) 73D, 99 (1994)] which controls the evolution through the scales of the probability density function of temperature increments. This equation, which needs some closure as well as initial data, uses results from direct numerical simulations or from experiments. For the dissipative and small inertial range scales, our predictions are in excellent agreement with the measured or numerically calculated probability density functions. The associated Yaglom equation is also well verified for the same range of scales.