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

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 veloc ity and passive temperature fluctuations are measured locally on the center line of the cylinder wake. The focus is on the scaling properties of the mi xed 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 th e same scaling behavior as [\ delta u(r) delta theta(r)(2)\]Psi(p)/Psi(3) o ver an extended range of scales. This yields accurate measurements for the relative scaling exponents Psi(p)/Psi(3). It is further observed that the m oments 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, 3 36 (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 gener alized similarity relation is well supported by our measurements over a ran ge of scales which greatly exceeds the inertial range. A theoretical predic tion is finally proposed, Psi(p) = p/9 + (10/9) (1 - (2/5)(p/3)), in good a greement with our experimental data. (C) 1999 American Institute of Physics , [S1070-6631(99)02207-2].