Anomalous self-similarity in two-dimensional turbulence

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, δv(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, 〈[δv(r)]p〉 ∼ rζp , exhibit anomalous scaling: ζp = p 2 rather than ζp = p 3 as in the 1941 Kolmogorov