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Effect of Schmidt number on the velocity–scalar cospectrum in isotropic turbulence with a mean scalar gradient

O'Gorman, P. A. and Pullin, D. I. (2005) Effect of Schmidt number on the velocity–scalar cospectrum in isotropic turbulence with a mean scalar gradient. Journal of Fluid Mechanics, 532 . pp. 111-140. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:OGOjfm05

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Abstract

We consider transport of a passive scalar by an isotropic turbulent velocity field in the presence of a mean scalar gradient. The velocity–scalar cospectrum measures the distribution of the mean scalar flux across scales. An inequality is shown to bound the magnitude of the cospectrum in terms of the shell-summed energy and scalar spectra. At high Schmidt number, this bound limits the possible contribution of the sub-Kolmogorov scales to the scalar flux. At low Schmidt number, we derive an asymptotic result for the cospectrum in the inertial–diffusive range, with a -11/3 power law wavenumber dependence, and a comparison is made with results from large-eddy simulation. The sparse direct-interaction perturbation (SDIP) is used to calculate the cospectrum for a range of Schmidt numbers. The Lumley scaling result is recovered in the inertial–convective range and the constant of proportionality was calculated. At high Schmidt numbers, the cospectrum is found to decay exponentially in the viscous–convective range, and at low Schmidt numbers, the -11/3 power law is observed in the inertial–diffusive range. Results are reported for the cospectrum from a direct numerical simulation at a Taylor Reynolds number of 265, and a comparison is made at Schmidt number order unity between theory, simulation and experiment.


Item Type:Article
Additional Information:Copyright © 2005 Cambridge University Press. Reprinted with permission. (Received 29 June 2004 and in revised form 14 December 2004) Published online 27 May 2005 P.A.OG. and D.I.P. were supported in part by the National Science Foundation under Grant CTS-0227881. The DNS was performed on the QSC supercomputer, and was supported by the Academic Strategic Alliances Program of the Accelerated Strategic Computing Initiative (ASCI/ASAP) under subcontract no. B341492 of DOE contract W-7405-ENG-48.
Subject Keywords:DIRECT-INTERACTION APPROXIMATION; LAGRANGIAN RENORMALIZED APPROXIMATION; QUANTITIES LIKE TEMPERATURE; LARGE-EDDY SIMULATION; SUBGRID-STRESS MODEL; PASSIVE SCALAR; STRATIFIED TURBULENCE; INERTIAL RANGE; FINE-STRUCTURE; SPECTRUM
Record Number:CaltechAUTHORS:OGOjfm05
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:OGOjfm05
Alternative URL:http://dx.doi.org/10.1017/S0022112005003903
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5066
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:26 Sep 2006
Last Modified:26 Dec 2012 09:03

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