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.