TY - JOUR

T1 - Statistics and geometry of passive scalars in turbulence

AU - Schumacher, Jörg

AU - Sreenivasan, Katepalli R.

N1 - Funding Information:
The computations were carried out on up to 256 IBM Power4 CPUs of the Jülich Multiprocessor (JUMP) machine at the John von Neumann-Institute for Computing of the Research Centre Jülich (Germany). The authors acknowledge their steady support, and the support by the Deutsche Forschungsgemeinschaft (J.S.) and by the U.S. National Science Foundation (J.S. and K.R.S.). J.S. thanks the Institute for Pure and Applied Mathematics at UCLA for hospitality during the Multiscale Geometric Analysis program, where parts of this work were done. The authors also thank R. W. Bilger, W. J. A. Dahm, J. Davoudi, J. A. Domaradzki, B. Eckhardt, S. B. Pope, and P. K. Yeung for useful discussions.

PY - 2005/12

Y1 - 2005/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=31144436205&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=31144436205&partnerID=8YFLogxK

U2 - 10.1063/1.2140024

DO - 10.1063/1.2140024

M3 - Article

AN - SCOPUS:31144436205

SN - 1070-6631

VL - 17

SP - 1

EP - 9

JO - Physics of Fluids

JF - Physics of Fluids

IS - 12

M1 - 125107

ER -