Anomalous self-similarity in two-dimensional turbulence

Abstract

Our velocity measurements on a quasi-two-dimensional turbulent flow in a rapidly rotating annulus yield an inverse cascade with E(k)~k^{-2} rather than the expected E(k)~k^{-5/3}. The probability distribution functions for longitudinal velocity differences, δ_v(r)=v(x+r)-v(x), are self-similar (scale independent) but strongly non-Gaussian, which suggests that the coherent vortices play a significant role. The structure functions, <[δ_v(r)]^p>~r^{ζ_p}, exhibit anomalous scaling: ζ_p=p/2 rather than ζ_p=p/3 as in the 1941 Kolmogorov theory.