An experimental observation of chaos arising from the interaction of steady and time-dependent flows

Abstract

APPLICATION of the results from studies of finite-dimensional dynamical systems to the understanding of turbulence in fluid flows is an area of great current interest. A complete description of turbulence is, however, still lacking, although new and interesting ideas continue to emerge¹. There have been some notable successes in the description of the evolution of temporal chaos in small-scale fluid-flow experiments, for example, in terms of period doubling^2,3. Here we present experimental results from a study of fluid motion between concentric rotating cylinders (Taylor-Couette flow). We have used laser techniques to explore the velocity field of the fluid as it proceeds from regular to weakly chaotic motion when an external control parameter is varied. We have applied modern signal-processing techniques to the velocity time series to identify temporal structures in the flow field. The evolution of these features is qualitatively the same as that found in sets of equations of much simpler form than those governing the motion of fluid flows. Our results provide striking evidence in support of the claim, as yet unproven, that there is a connection between the Navier-Stokes equations of fluid motion and properties of finite-dimensional dynamical systems.