Statistics and geometry of passive scalars in turbulence

Jörg Schumacher, Katepalli R. Sreenivasan

Research output: Contribution to journalArticle

Abstract

We present direct numerical simulations of the mixing of the passive scalar at modest Taylor microscale (10≤Rλ≤42) and Schmidt numbers larger than unity (2≤Sc≤32). The simulations resolve below the Batchelor scale up to a factor of 4. The advecting turbulence is homogeneous and isotropic, and is maintained stationary by stochastic forcing at low wave numbers. The passive scalar is rendered stationary by a mean scalar gradient in one direction. The relation between geometrical and statistical properties of scalar field and its gradients is examined. The Reynolds numbers and Schmidt numbers are not large enough for either the Kolmogorov scaling or the Batchelor scaling to develop and, not surprisingly, we find no fractal scaling of scalar level sets, or isosurfaces, in the intermediate viscous range. The area-to-volume ratio of isosurfaces reflects the nearly Gaussian statistics of the scalar fluctuations. The scalar flux across the isosurfaces, which is determined by the conditional probability density function (PDF) of the scalar gradient magnitude, has a stretched exponential distribution towards the tails. The PDF of the scalar dissipation departs distinctly, for both small and large amplitudes, from the log-normal distribution for all cases considered. The joint statistics of the scalar and its dissipation rate, and the mean conditional moment of the scalar dissipation, are studied as well. We examine the effects of coarse-graining on the probability density to simulate the effects of poor probe-resolution in measurements.

Original languageEnglish (US)
Article number125107
Pages (from-to)1-9
Number of pages9
JournalPhysics of Fluids
Volume17
Issue number12
DOIs
StatePublished - Dec 2005

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Probability density function
Turbulence
turbulence
Statistics
statistics
scalars
Geometry
Direct numerical simulation
Normal distribution
geometry
Fractals
Reynolds number
Fluxes
Schmidt number
dissipation
probability density functions
scaling
gradients
homogeneous turbulence
isotropic turbulence

ASJC Scopus subject areas

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

Cite this

Statistics and geometry of passive scalars in turbulence. / Schumacher, Jörg; Sreenivasan, Katepalli R.

In: Physics of Fluids, Vol. 17, No. 12, 125107, 12.2005, p. 1-9.

Research output: Contribution to journalArticle

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