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

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 [\ delta u(r) delta theta(r)(2)\(p/3)]. It is observed that [\ delta u(r) delta theta(r)(2)\(p/3)] displays the same scaling behavior as [\ delta u(r) delta theta(r)(2)\]Psi(p)/Psi(3) over an extended range of scales. This yields accurate measurements for the relative scaling exponents Psi(p)/Psi(3). 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 Leveque [Phys. Rev. Lett. 72, 336 (1994)]. Otherwise it is Proposed that [\ delta u(r)delta theta(r)(2)\(p/3)] scales as [N(r)(p/3)][\ delta u(r)delta theta(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, Psi(p) = p/9 + (10/9) (1 - (2/5)(p/3)), in good agreement with our experimental data. (C) 1999 American Institute of Physics, [S1070-6631(99)02207-2].