Reemergent Order of Chaotic Circular Couette Flow

Abstract

Measurements of the fluctuations in local velocity in fluid motion between a rotating inner cylinder and a fixed outer cylinder are reported for rotation rates up to $67{R}_{c}$, where ${R}_{c}$ is the critical Reynolds number for Taylor instability. The Reynolds number ${R}_{t}$ for which the transition from periodic or quasiperiodic to aperiodic flow occurs depends strongly on aspect ratio ($\ensuremath{\Gamma}=\mathrm{fluid}\mathrm{height}/\mathrm{gap}$): ${R}_{t}\ensuremath{\simeq}22{R}_{c}$ for $\ensuremath{\Gamma}=20$; ${R}_{t}\ensuremath{\simeq}26{R}_{c}$ for $\ensuremath{\Gamma}=80$. For $\ensuremath{\Gamma}\ensuremath{\gtrsim}25$ a sharp periodic component reemerges in the power spectrum for $28{R}_{c}\ensuremath{\lesssim}R\ensuremath{\lesssim}36{R}_{c}$.