On the universality of anomalous scaling exponents of structure functions in turbulent flows

Ewe-Wei Saw 1, 2 Paul Debue 1 Denis Kuzzay 1 François Daviaud 1 Bérengère Dubrulle 1, *
* Corresponding author
1 SPHYNX - Systèmes Physiques Hors-équilibre, hYdrodynamique, éNergie et compleXes
SPEC - UMR3680 - Service de physique de l'état condensé, IRAMIS - Institut Rayonnement Matière de Saclay
Abstract : All previous experiments in open turbulent flows (e.g. downstream of grids, jets and the atmospheric boundary layer) have produced quantitatively consistent values for the scaling exponents of velocity structure functions (Anselmet et al., J.). The only measurement of scaling exponents at high order (>6) in closed turbulent flow (von Kármán swirling flow) using Taylor's frozen flow hypothesis, however, produced scaling exponents that are significantly smaller, suggesting that the universality of these exponents is broken with respect to change of large scale geometry of the flow. Here, we report measurements of longitudinal structure functions of velocity in a von Kármán setup without the use of the Taylor hypothesis. The measurements are made using stereo particle image velocimetry at four different ranges of spatial scales, in order to observe a combined inertial subrange spanning approximately one and a half orders of magnitude. We found scaling exponents (up to ninth order) that are consistent with values from open turbulent flows, suggesting that they might be in fact universal.
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Ewe-Wei Saw, Paul Debue, Denis Kuzzay, François Daviaud, Bérengère Dubrulle. On the universality of anomalous scaling exponents of structure functions in turbulent flows. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2018, 837, pp.657 - 669. ⟨10.1017/jfm.2017.848⟩. ⟨cea-01687769⟩

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