Scalings and structures in turbulent Couette-Taylor flow

The scaling of velocity structure functions in Couette-Taylor flow [Lewis and Swinney, Phys. Rev. E $59,$ 5457 (1999)] is revisited to obtain more accurate values of the scaling exponents for the Reynolds number range investigated, 12 000 to 540 000 (Taylor Reynolds numbers, $34<\mathrm{}{R}_{\lambda }<220).\mathrm{}$ Systematic convergence of the statistics with increasing sample size is examined, and the uncertainty of the scaling exponents is assessed. At all Reynolds numbers the data support the hierarchical symmetry proposed by She and Leveque [Phys. Rev. Lett. $72,$ 336 (1994)]. The She-Leveque constant $\beta$ has a value of 0.83, indicating greater intermittency in Couette-Taylor turbulence than in free jets, where $\beta =\mathrm{0.87.}\mathrm{}$ The constant $\gamma ,$ which is a measure of the degree of singularity of the most intermittent structure, decreases from 0.14 for $R<\mathrm{}{10}^5$ to 0.10 for $R>\mathrm{}{10}^5;$ this transition corresponds to a visually observed break up of the Taylor vortex roll structure with increasing R.