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.