Journal of Fluid Mechanics

Experimental study of the fine-scale structure of conserved scalar mixing in turbulent shear flows. Part 1. Sc [dbl greater-than sign] 1

Kenneth A.  Buch Jr. a1p1 and Werner J. A.  Dahm a1
a1 Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI 48109-2118, USA

Article author query
buch ka   [Google Scholar] 
dahm wj   [Google Scholar] 


We present results from an experimental investigation into the fine-scale structure associated with the mixing of a dynamically passive conserved scalar quantity on the inner scales of turbulent shear flows. The present study was based on highly resolved two- and three-dimensional spatio-temporal imaging measurements. For the conditions studied, the Schmidt number (Sc [identical with] v/D) was approximately 2000 and the local outerscale Reynolds number (Reσ [identical with] uσ/v) ranged from 2000 to 10000. The resolution and signal quality allow direct differentiation of the measured scalar field ζ(x, t) to give the instantaneous scalar energy dissipation rate field (Re Sc)−1 [nabla del, Hamilton operator]ζc[nabla del, Hamilton operator]ζ(x, t). The results show that the fine-scale structure of the scalar dissipation field, when viewed on the inner-flow scales for Sc [identical with] 1, consists entirely of thin strained laminar sheet-like diffusion layers. The internal structure of these scalar dissipation sheets agrees with the one-dimensional self-similar solution for the local strain–diffusion competition in the presence of a spatially uniform but time-varying strain rate field. This similarity solution also shows that line-like structures in the scalar dissipation field decay exponentially in time, while in the vorticity field both line-like and sheet-like structures can be sustained. This sheet-like structure produces a high level of intermittency in the scalar dissipation field – at these conditions approximately 4% of the flow volume accounts for nearly 25% of the total mixing achieved. The scalar gradient vector field [nabla del, Hamilton operator]ζ(x, t) for large Sc is found to be nearly isotropic, with a weak tendency for the dissipation sheets to align with the principal axes of the mean flow strain rate tensor. Joint probability densities of the conserved scalar and scalar dissipation rate have a shape consistent with this canonical layer-like fine-scale structure. Statistics of the conserved scalar and scalar dissipation rate fields are found to demonstrate similarity on inner-scale variables even at the relatively low Reynolds numbers investigated.

(Published Online April 26 2006)
(Received January 20 1995)
(Revised November 1 1995)

p1 Present address: Sandia National Laboratories, Diagnostic and Reacting Flow Department, PO Box 969, MS 9051, Livermore, CA 94551-0969, USA.