0
Special Section Articles

The Turbulent Schmidt Number

[+] Author and Article Information
Diego A. Donzis

Assistant Professor
Mem. ASME
Department of Aerospace Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: donzis@tamu.edu

Konduri Aditya

Graduate Research Assistant
Department of Aerospace Engineering,
Texas A&M University,
College Station, TX 77843

K. R. Sreenivasan

Professor
Fellow ASME
Departments of Physics and
Mechanical Engineering and
Courant Institute of Mathematical Sciences,
New York University,
New York, NY 10012

P. K. Yeung

Professor
Fellow ASME
School of Aerospace Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332;
Department of Mechanical and
Aerospace Engineering,
Hong Kong University of
Science and Technology,
Clear Water Bay, Hong Kong

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 12, 2013; final manuscript received January 28, 2014; published online April 28, 2014. Assoc. Editor: Ye Zhou.

J. Fluids Eng 136(6), 060912 (Apr 28, 2014) (5 pages) Paper No: FE-13-1554; doi: 10.1115/1.4026619 History: Received September 12, 2013; Revised January 28, 2014

We analyze a large database generated from recent direct numerical simulations (DNS) of passive scalars sustained by a homogeneous mean gradient and mixed by homogeneous and isotropic turbulence on grid resolutions of up to 40963 and extract the turbulent Schmidt number over large parameter ranges: the Taylor microscale Reynolds number between 8 and 650 and the molecular Schmidt number between 1/2048 and 1024. While the turbulent Schmidt number shows considerable scatter with respect to the Reynolds and molecular Schmidt numbers separately, it exhibits a sensibly unique functional dependence with respect to the molecular Péclet number. The observed functional dependence is motivated by a scaling argument that is standard in the phenomenology of three-dimensional turbulence.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 2

Turbulent Schmidt number versus molecular Schmidt number. Circles and squares correspond to EP and FEK forcing, respectively. The relative sizes of symbols indicate the relative values of Rλ.

Grahic Jump Location
Fig. 1

Turbulent Schmidt number versus the microscale Reynolds number. Circles and squares correspond to EP and FEK forcing, respectively. The relative sizes of symbols indicate the relative value of Sc. Open and filled symbols correspond to data for Sc ≤ 1 and Sc > 1, respectively. Dashed line at 1.18 is the mean of data with Sc > 1 and Rλ > 30 (see text below).

Grahic Jump Location
Fig. 4

Turbulent Schmidt number versus Péclet number. Circles and squares correspond to EP and FEK forcing, respectively. The relative sizes of symbols indicate to the relative value of Sc. Open and filled symbols correspond to Sc ≤ 1 and Sc > 1. Data from other studies include diamonds: Overholt and Pope [15] and triangles: Gotoh and Watanabe [9]. Dashed line is the average of all data with Pe > 1000. Dash-dotted line corresponds to Eq. (7) with c1 = 1.36 and c2 ≈ 13.

Grahic Jump Location
Fig. 3

Normalized scalar flux spectrum Euφ(k)/G〈ɛ〉1/3η7/3. This normalized form tends to (kη)-7/3 in the inertial-convective consistent with Ref. [17]. (a) Fixed Sc = 1 with Rλ ≈ 8, 140, 400, and 650. (b) Fixed Rλ ≈ 140 with Sc =1/8, 1, 8, and 32. Dashed lines with slope −7/3 are drawn for reference.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In