Velocity structure functions, scaling, and transitions in high-Reynolds-number Couette-Taylor flow

Flow between concentric cylinders with a rotating inner cylinder is studied for Reynolds numbers in the range $2\times {10}^3<R<\mathrm{}{10}^6$ (Taylor Reynolds numbers, $10<\mathrm{}{R}_{\lambda }<290)$ for a system with radius ratio $\eta =0.724\mathrm{}$. Even at the highest Reynolds number studied, the energy spectra do not show power law scaling (i.e., there is no inertial range), and the dissipation length scale is surprisingly large. Nevertheless, the velocity structure functions calculated using extended self-similarity exhibit clear power-law scaling. The structure function exponents ${\zeta }_p$ fit Kolmogorov’s log-normal model within the experimental uncertainty, ${\zeta }_p=(p/3\mathrm{})\mathrm{}[1+(\mu /6\left)\right(3\mathrm{}-p\left)\right]$ (for $p<~10)$ with $\mu =0.27\mathrm{}$. These ${\zeta }_p$ values are close to those found in other flows. Measurements of torque scaling are presented that are an order of magnitude more accurate than those previously reported [Lathrop et al., Phys Rev. A 46, 6390 (1992)]. Measurements of velocity in the fluid core reveal the presence of azimuthal traveling waves up to the highest Reynolds numbers examined. These waves show evidence of a transition at $R_T=1.3\mathrm{}\times {10}^4$; this transition was observed previously in measurements of torque, but our wave velocity and wall shear stress measurements provide the first evidence from local quantities of the transition at $R_T.$ Velocity measurements indicate that at $R_T$ there is a change in the coherent structures of the core flow; this is consistent with our analyses of the scaling of the torque. Our measurements were made at two aspect ratios, and no significant dependence on aspect ratio was observable for $R>\mathrm{}{R}_T.$