Nonextensivity in turbulence in rotating two-dimensional and three-dimensional flows

Our experiments on turbulent flow in a rotating annulus yield probability distribution functions (PDFs) for velocity increments δv(ℓ), where ℓ is the separation between points. We fit these PDFs to a form derived for turbulent flows by Beck, who used the Tsallis nonextensive statistical mechanics formalism. For slow rotation rates, we find that the fit parameter q is 1.25 for small ℓ. At large ℓ, q decreases to unity, the value corresponding to the usual Boltzmann-Gibbs statistics. These results agree with those previously measured in experiments on Couette-Taylor turbulence. However, with rapid rotation of the annulus, the turbulent flow becomes strongly two-dimensional (2D) rather than three-dimensional (3D), and we find q=1.32±0.04, independent of ℓ. This suggests that the coherent structures (vortices), which are a source of intermittency, are important at all length scales in the 2D case.