### Abstract

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 ≡ ν/D) was approximately 2000 and the local outer-scale Reynolds number (Re_{δ} ≡ uδ/ν) ranged from 2000 to 10000. The resolution and signal quality allow direct differentiation of the measured scalar field ξ(x, t) to give the instantaneous scalar energy dissipation rate field (Re Sc)^{-1}∇ζ·∇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 ≫ 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 ∇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.

Original language | English (US) |
---|---|

Pages (from-to) | 21-71 |

Number of pages | 51 |

Journal | Journal of Fluid Mechanics |

Volume | 317 |

State | Published - Jun 25 1996 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

**Experimental study of the fine-scale structure of conserved scalar mixing in turbulent shear flows. Part 1. Sc ≫ 1.** / Buch, Kenneth A.; Dahm, Werner.

Research output: Contribution to journal › Article

*Journal of Fluid Mechanics*, vol. 317, pp. 21-71.

}

TY - JOUR

T1 - Experimental study of the fine-scale structure of conserved scalar mixing in turbulent shear flows. Part 1. Sc ≫ 1

AU - Buch, Kenneth A.

AU - Dahm, Werner

PY - 1996/6/25

Y1 - 1996/6/25

N2 - 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 ≡ ν/D) was approximately 2000 and the local outer-scale Reynolds number (Reδ ≡ uδ/ν) ranged from 2000 to 10000. The resolution and signal quality allow direct differentiation of the measured scalar field ξ(x, t) to give the instantaneous scalar energy dissipation rate field (Re Sc)-1∇ζ·∇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 ≫ 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 ∇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.

AB - 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 ≡ ν/D) was approximately 2000 and the local outer-scale Reynolds number (Reδ ≡ uδ/ν) ranged from 2000 to 10000. The resolution and signal quality allow direct differentiation of the measured scalar field ξ(x, t) to give the instantaneous scalar energy dissipation rate field (Re Sc)-1∇ζ·∇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 ≫ 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 ∇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.

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M3 - Article

VL - 317

SP - 21

EP - 71

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -