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REVIEW ARTICLES

Effect of Schmidt number on small-scale passive scalar turbulence

[+] Author and Article Information
RA Antonia

Discipline of Mechanical Engineering, University of Newcastle, NSW, 2308, Australiameraa@cc.newcastle.edu.au

P Orlandi

Dipartimento di Meccanica e Aeronautica, Universita Degli Studi di Roma “La Sapienza,” 00184 Rome, Italyorlandi@kolmogorov.ing.uniroma1.it

Appl. Mech. Rev 56(6), 615-632 (Nov 26, 2003) (18 pages) doi:10.1115/1.1581885 History: Online November 26, 2003
Copyright © 2003 by ASME
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Figures

Grahic Jump Location
Schematic representation, adapted from Fig. 8.11 in Tenekes and Lumley 33, of the various ranges in the 3D scalar spectrum for Sc≃1,Sc≫1 and Sc≪1
Grahic Jump Location
Comparison between DNS and measured Kolmogorov-normalized 1D spectra of u1,u2, and θ at Sc≃0.7(Rλ≃50).a) u1;b) u2;c) θ. –, measured 90; [[dashed_line]], 88.
Grahic Jump Location
Comparison between DNS and measured Batchelor-normalized 1D scalar spectra at Sc≃7. [[long_dash_short_dash]], 103, 3843 simulation of decaying homogeneous isotropic turbulence (Rλ≃50). ○, 62(Rλ≃80); □, 8(Rλ≃220). The solid line has a slope of −1.
Grahic Jump Location
DNS Batchelor-normalized 3D scalar spectra at different values of Sc. Data of 103: ––, Sc=0.07; [[dashed_line]], 0.3; — - —, 0.7; — -- —, 1; –––  –––, 3; — —, 7. The straight lines correspond to a k−1 ([[dashed_line]]) and k−5/3 (–) power-laws.
Grahic Jump Location
Comparison between DNS Batchelor-normalized 3D scalar spectra obtained by different investigators over a wide range of Sc.25 (stationary): ▵, Sc=0.7(Rλ=95); ▿, 25 (46); •, 7 (46); ▪, 1 (46); +, 0.1 (95); ⊞, 0.04 (130); ○, 144 (22). 25 (decaying): □, Sc=144(Rλ=22).23Sc=1: ––, forced (Rλ=151); — —, decaying (Rλ=132).103 (decaying): –––, Sc=7(Rλ≃50). The solid line has a slope of “−1.”
Grahic Jump Location
Dependence of measured and DNS values of ST, the mixed velocity-scalar derivative skewness on Sc. Experiments: ▵, 8; ⊖, 74; ⊟, 90. DNS data (stationary turbulence): □, 14; ▿, 22; +, 23; ⋄, 28. DNS data (decaying turbulence): •, 88.
Grahic Jump Location
Dependence on Sc of the Batchelor-normalized variance of the scalar derivative. DNS data (decaying turbulence) from 88. ○, i=1; □, i=2; ▿, i=3.
Grahic Jump Location
Dependence of Sc on the ratio of variances of the scalar derivatives in directions parallel and perpendicular to the imposed mean scalar gradient. 19: •, Rλ=45; ▪, 67. 26: ○, Rλ=46; □, 95; ▿, 130. 28: ▵, Rλ=38.
Grahic Jump Location
Dependence on Sc of the skewness of the scalar derivative in a direction parallel to the imposed mean scalar gradient. 19: •, Rλ=45; ▪, 67. 26: ○, Rλ=46; □, 95; ▿, 130. 28: ▵, Rλ=38.
Grahic Jump Location
Dependence on Sc of kurtosis of the scalar derivative in a direction parallel to the imposed mean scalar gradient. 19: •, Rλ=45; ▪, 67. 26: ○, Rλ=46; □, 95; ▿, 130. 28: ▵, Rλ=38.
Grahic Jump Location
Isocontours, in a 2D plane, of θ and its derivative, obtained by Brethouwer et al. 26. Isocontours of θ: (a) Sc=0.7; (c) Sc=25. Isocontours of ∇θ: (b) Sc=25; (d) Sc=0.7.
Grahic Jump Location
Probability density function of the scalar concentration in decaying isotropic turbulence from DNS data of 88. +, Sc=0.07; ×, 0.3;  * , 0.7; □, 1; ▵, 3; ○, 7.; [[long_dash_short_dash]], Gaussian distribution.
Grahic Jump Location
Probability density function of the scalar concentration in the wake of a circular cylinder. Reconstructed from data of13. ○, Sc≃2000,x/d=225; □, 0.7, 300. — - —, Gaussian distribution.
Grahic Jump Location
2D contours of ln(ε/〈ε〉) and ln(χ/〈χ〉) for three values of Sc and joint probability density functions between ln ε and ln χ. Data are from 88. Top to bottom Sc=0.07, 0.7, 7. In the contour plots, the solid lines refer to ln(ε/〈ε〉) and the color contours are for ln(χ/〈χ〉).

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