Schmidt number dependence of derivative moments for quasistatic straining motion

Abstract

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, whose $Sc$ varies between 1/4 and 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. This paper has been withdrawn by the authors due to copyright. It appears in Journal of Fluid Mechanics (2003). http://jfm-www.damtp.cam.ac.uk/