Anomalous Self-Similarity in a Turbulent Rapidly Rotating Fluid

Our velocity measurements on quasi-two-dimensional turbulent flow in a rapidly rotating annulus yield self-similar (scale-independent) probability distribution functions for longitudinal velocity differences, δv()0ex0ex=0ex0exv(x+)-v(x). These distribution functions are strongly non-Gaussian, suggesting that the coherent vortices play a significant role. The structure functions 〈[δv()]ᵖ〉~^ζₚ exhibit anomalous scaling: ζₚ0ex0ex=0ex0exp/2 rather than the expected ζₚ0ex0ex=0ex0exp/3. Correspondingly, the energy spectrum is described by E(k)~k^-2 rather than the expected E(k)~k^-5/3.