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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.

In this paper the linear stability of a fluid layer flowing down the inside and outside of a rotating vertical cylinder is investigated. To this end, two approximations are made: the small wave number approximation and the small Reynolds number approximation. In the former, only the radial destabilizing effect of surface tension is important and may be counteracted by the centrifugal force at a critical value. In the latter, the analysis integrates the azimuthal modes different from m=0. It is shown that for flow outside the cylinder, the magnitude of centrifugal force and wave number may change the dominant mode of instability. For flow inside the cylinder, only the mode m=0 may be unstable. These results generalize those of Boudourides and Davis [Z. Angew. Math. Phys. 37, 597 (1986)] for swirling viscous flows.