Scaling laws for the turbulent mixing of a passive scalar in the wake of a cylinder

Abstract

Turbulence is triggered by an air flow passing around a cylinder and heated by an array of hot wires parallel to the cylinder axis. Simultaneous velocity and passive temperature fluctuations are measured locally on the centerline of the cylinder wake. The focus is on the scaling properties of the mixed scalar-velocity structure functions 〈|δu(r)δθ(r)2|p/3〉. It is observed that 〈|δu(r)δθ(r)2|p/3〉 displays the same scaling behavior as 〈|δu(r)δθ(r)2|〉Ψp/Ψ3 over an extended range of scales. This yields accurate measurements for the relative scaling exponents Ψp/Ψ3. It is further observed that the moments of the coarse-grained scalar energy diffusion rate 〈N(r)p〉 satisfy a closure condition as proposed by She and Lévêque [Phys. Rev. Lett. 72, 336 (1994)]. Otherwise it is proposed that 〈|δu(r)δθ(r)2|p/3〉 scales as 〈N(r)p/3〉〈|δu(r)δθ(r)2|〉p/3. This generalized similarity relation is well supported by our measurements over a range of scales which greatly exceeds the inertial range. A theoretical prediction is finally proposed, Ψp=p/9+(10/9)(1−(2/5)p/3), in good agreement with our experimental data.

Fronts in passive scalar turbulence

“…We consider moments |Π r | p ∼ r αp , which have been studied in the context of experimental turbulence in Ref. [53]. As shown in Figure 27, the computed scaling exponents α p deviate significantly from the dimensional prediction α p = p. The behavior of the exponents for large orders can be explained with the aid of the results of Section VIII.…”

Universal hierarchical symmetry for turbulence and general multi-scale fluctuation systems

“…The following year, Camussi and Benzi [17] concluded that the SL prediction was realized in all cases, confirming that, within the experimental uncertainty, the geometrical interpretation of β could be extended to the transverse velocity components (see also Benzi et al [18,19] for more details). Leveque et al [20] observed, in a turbulent wake, that the moments of passive scalar energy diffusion rate satisfy a similar hierarchical symmetry relation. The evidences from all these classical experiments offer a solid basis for the validity of the SL hierarchical symmetry, and provides enough stimulation for continuous interests later on further checks, modifications and applications.…”

Exit-times and ϵ-entropy for dynamical systems, stochastic processes, and turbulence

“…Turbulence was generated by a cylinder placed inside the wind tunnel, its diameter was 0.1 m. The hot wire was placed 2.0 m behind the cylinder. The separation between both probes was approximately 1 mm [40]. The measurement in Modane has been taken in a wind tunnel where the integral scale was L ∼ 20 m and the dissipative scale was r diss = 0.3 mm.…”