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, $\delta v\left(\ell \right)=v(x+\ell )-v\left(x\right)$. These distribution functions are strongly non-Gaussian, suggesting that the coherent vortices play a significant role. The structure functions $〈\left[\delta v\right(\ell ){]}^p〉\sim {\ell }^{{\zeta }_p}$ exhibit anomalous scaling: ${\zeta }_p=\frac{p}{2}$ rather than the expected ${\zeta }_p=\frac{p}{3}$. Correspondingly, the energy spectrum is described by $E\left(k\right)\sim k^{-2\mathrm{}}$ rather than the expected $E\left(k\right)\sim k^{-5/3\mathrm{}}$.