The mixing transition in turbulent flows

Creators: Dimotakis, Paul E.

Abstract

Data on turbulent mixing and other turbulent-flow phenomena suggest that a (mixing) transition, originally documented to occur in shear layers, also occurs in jets, as well as in other flows and may be regarded as a universal phenomenon of turbulence. The resulting fully-developed turbulent flow requires an outer-scale Reynolds number of Re = U[delta]/v [greater, similar] 1–2 × 104, or a Taylor Reynolds number of ReT = u[prime prime or minute] [lambda]T/v [greater, similar] 100–140, to be sustained. A proposal based on the relative magnitude of dimensional spatial scales is offered to explain this behaviour.

Additional Information

"Reprinted with the permission of Cambridge University Press." (Received January 15 1999) (Revised May 15 1999) Published Online 08Sep2000 This paper was prepared in honour of P. G. Saffman. I would like to acknowledge the work and discussions on this topic with P. L. Miller, and his assistance with the text, as well as the critical reading and suggestions by D. I. Pullin. This work was supported under AFOSR Grant Nos. F49620-94-1-0353 and F49620-98-1-0052. A first version of the data compilation and ideas presented here was documented by the author (1993) as a GALCIT Report. Note added in proof: A. Domaradzki has brought to my attention (private communication) that the original observation by Heslot et al. (1987) that convective turbulence experiences a transition at Ra ~ 4 x 10^7 (cf. discussion on p. 86, herein) may be attributed to a near-unity aspect ratio in those experiments. For high aspect ratios, most signs of that transition, including the change in scaling exponents, disappear, or move to much lower values of Ra (cf. discussion in Christie & Domaradzki 1993, 1994).

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