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Schmidt number dependence of derivative moments for quasi-static straining motion

Published online by Cambridge University Press:  01 April 2003

J. SCHUMACHER ,
K. R. SREENIVASAN  and
P. K. YEUNG
J. SCHUMACHER
Affiliation:
Fachbereich Physik, Philipps-Universität, D-35032 Marburg, Germany
K. R. SREENIVASAN
Affiliation:
Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA
P. K. YEUNG
Affiliation:
School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
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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, 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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 479 , 25 March 2003 , pp. 221 - 230
Copyright
© 2003 Cambridge University Press

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