Absolute and convective instabilities and noise-sustained structures in the Couette-Taylor system with an axial flow.

Abstract

A detailed study of the Couette-Taylor system with axial flow in the range of Reynolds number Re up to 4.5, which is characterized by the propagating Taylor-vortices (PTV's) state, is presented. Two methods to measure the convective instability line are described. Comparative studies of the PTV's in the absolutely and convectively unstable regions are given. It was found that at Re1 the PTV's appear first at the outlet at the absolute instability transition. At Re>1 the PTV's are also sustained in the convectively unstable region, but the properties of the PTV's in the absolutely and convectively unstable regions differ distinctively. In both regions the PTV's are characterized by the existence of an interface separating the pattern state from the Couette-Poiseuille flow. The interface is stationary in the absolutely unstable region and fluctuates in the convectively unstable region. The distance from the inlet to the interface changes as both control parameters \ensuremath{\epsilon}\ifmmode\bar\else\textasciimacron\fi{} and Re are varied, where \ensuremath{\epsilon}\ifmmode\bar\else\textasciimacron\fi{} is the distance from the convective line. This dependence is, however, different in both regions. In the absolutely unstable region the healing length is scaled with the PTV's group velocity at all values of \ensuremath{\epsilon}\ifmmode\bar\else\textasciimacron\fi{} and Re, and diverges at the absolute instability transition line. In the convectively unstable region the healing length does not obey the general scaling but is about inversely proportional to \ensuremath{\epsilon}\ifmmode\bar\else\textasciimacron\fi{}. The most distinctive difference in the PTV's behavior in the two regions is a different sensitivity to noise.A time-dependent spatial profile of the PTV's leads to a broadband power spectrum of the velocity in the convectively unstable region near the outlet. The PTV's velocity power spectrum in the absolutely unstable region is, on the other hand, noise-free. The different sensitivity to noise was used as an experimental criterion to locate the absolute instability line for Re>1. The wave-number selection is also found to be different in both regions. As a result, we concluded that the PTV's in the convectively unstable region are noise-sustained structures (NSS's) which were recently considered theoretically and observed in numerical simulations. The selective spatial amplification of an external noise and the characteristic dependence of the healing length on the control parameters and on the aspect ratio confirm our suggestion that the mechanism of NSS generation is a selective spatial amplification of a permanent noise at the inlet. An interaction of the noise with the NSS's leads to a noise modulation of the PTV's velocity.