Schmidt Number Dependence Of Derivative Moments For Quasi-Static Straining Motion

Bounds on high-order derivative moments of a passive scalar are obtained for large values of the Schmidt number, Sc. The procedure is based on the approach pioneered by Batchelor for the viscous-convective range. The upper bounds for derivative moments of order n are shown to grow as Sc^n/2 for very large Schmidt numbers. The results are consistent with direct numerical simulations of a passive scalar, with Sc from 1/4 to 64, mixed by homogeneous isotropic turbulence. Although the analysis does not provide proper bounds for normalized moments, the combination of analysis and numerical data suggests that they decay with Sc, at least for odd orders.