Schmidt number dependence of derivative moments for quasistatic straining motion

Details Schmidt number dependence of derivative moments for quasistatic straining motion Schmidt number dependence of derivative moments for quasistatic straining motion

2003-01-16

arxiv.org/abs/nlin/0301018v2

J. Fluid Mech., 479 (2003) 221

Nonlinear Sciences

Chaotic Dynamics

9 pages, 4 Postscript figures

Scientific paper

10.1017/S0022112003003756

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 This paper has been withdrawn by the authors due to copyright.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/

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