### Abstract

Results are presented from highly resolved dual-plane stereo particle image velocimetry (DSPIV) measurements for the structure, statistics, similarity, and scaling of all nine simultaneous components of the velocity gradient tensor fields ∂u_{i}∂x_{j} on the quasi-universal intermediate and small scales of turbulent shear flows. Measurements were obtained at three combinations of the outer-scale Reynolds number Re_{δ} and the local mean shear rate S in the fully developed self-similar far field of a turbulent jet, and thus reflect the combined effects of the large-scale structure, spatial inhomogeneities, and anisotropies inherent in such a flow. Conditions addressed in this study correspond to local outer-scale Reynolds numbers Re_{δ}=6,000 and 30,000 and local mean shear values Sδu_{u}c=0 and 1.7, corresponding to Taylor-scale Reynolds numbers Re_{λ} ≈44 and 113 and shear rates Sk/E=0 and 2.1. Gradient fields investigated here include the individual velocity gradient component fields, the strain rate component fields and the associated principal strain rates, the vorticity component fields and their orientations with respect to the principal strain axes, the enstrophy and enstrophy production rate fields, and the true kinetic energy dissipation rate field. Results normalized on both inner- and outer-scale variables are presented to allow interpretation relative to the similarity and scaling implied by classical turbulence theory. For both Re_{δ} values at S=0, results show that most aspects of these gradient fields are essentially in agreement with the predictions from homogeneous isotropic turbulence, while for S≠0 there are significant and consistent departures from isotropy. Results also provide direct measurements of the exponential scaling factors in the left and right tails of the velocity gradient distributions, as well as quantification of the inner (viscous) length scales in the enstrophy and dissipation rate fields. In addition, strong evidence for multifractal scale similarity at length scales greater than about twice the viscous length λ_{v} is found in both the enstrophy and dissipation rate fields.

Original language | English (US) |
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Article number | 035102 |

Journal | Physics of Fluids |

Volume | 18 |

Issue number | 3 |

DOIs | |

State | Published - Mar 2006 |

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### Keywords

- Flow visualisation
- Fractals
- Jets
- Shear turbulence
- Vortices

### ASJC Scopus subject areas

- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes