Schmidt number effects on turbulent transport with uniform mean scalar gradient

P. K. Yeung, Shuyi Xu, K. R. Sreenivasan

Research output: Contribution to journalArticle

Abstract

We study by direct numerical simulations the effects of Schmidt number (Sc) on passive scalars mixed by forced isotropic and homogeneous turbulence. The scalar field is maintained statistically stationary by a uniform mean gradient. We consider the scaling of spectra, structure functions, local isotropy and intermittency. For moderately diffusive scalars with Sc = 1/8 and 1, the Taylor-scale Reynolds number of the flow is either 140 or 240. A modest inertial-convective range is obtained in the spectrum, with a one-dimensional Obukhov-Corrsin constant of about 0.4, consistent with experimental data. However, the presence of a spectral bump makes a firm assessment somewhat difficult. The viscous-diffusive range is universal when scaled by Obukhov-Corrsin variables. In a second set of simulations we keep the Taylor-microscale Reynolds number fixed at 38 but vary Sc from 1/4 to 64 (a range of over two decades), roughly by factors of 2. We observe a gradual evolution of a - 1 roll-off in the viscous-convective region as Sc increases, consistent with Batchelor's predictions. In the viscous-diffusive range the spectra follow Kraichnan's form well, with a coefficient that depends weakly on Sc. The breakdown of local isotropy manifests itself through differences between structure functions with separation distances in directions parallel and perpendicular to the mean scalar gradient, as well as via finite values of odd-order moments of scalar gradient fluctuations and of mixed velocity-scalar gradient correlations. However, all these indicators show, to varying degrees, an increasing tendency to isotropy with increasing Sc. The moments of scalar gradients and the scalar dissipation rate peak at Sc ≈ 4. The intermittency exponent for the scale-range between the Kolmogorov and Batchelor scales is found to decrease with Sc, suggesting qualitative consistency with previous dye experiments in water [Sc = O(1000)].

Original languageEnglish (US)
Pages (from-to)4178-4191
Number of pages14
JournalPhysics of Fluids
Volume14
Issue number12
DOIs
StatePublished - Dec 2002

Fingerprint

Schmidt number
Reynolds number
scalars
gradients
Direct numerical simulation
isotropy
Turbulence
Coloring Agents
Dyes
Water
intermittency
Experiments
moments
homogeneous turbulence
isotropic turbulence
direct numerical simulation
microbalances
tendencies
dissipation
breakdown

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes
  • Computational Mechanics
  • Mechanics of Materials
  • Physics and Astronomy(all)
  • Condensed Matter Physics

Cite this

Schmidt number effects on turbulent transport with uniform mean scalar gradient. / Yeung, P. K.; Xu, Shuyi; Sreenivasan, K. R.

In: Physics of Fluids, Vol. 14, No. 12, 12.2002, p. 4178-4191.

Research output: Contribution to journalArticle

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