Transition to Turbulence via Spatiotemporal Intermittency: Modeling and Critical Properties

Abstract

When studying the transition to turbulence in closed flow systems, it has become traditional to make a distinction between them according to confinement effects. These effects can be measured by aspect-ratios, i.e. ratios of the lateral dimensions of the physical system to some internal length linked to the basic instability mechanism. Small aspect-ratio systems are strongly confined so that the spatial structure of the modes involved can be considered as frozen. As such, they experience a transition to turbulence according to scenarios understood in the framework of low dimensional dynamical systems theory. The general procedure in this field involves the reduction to center manifold dynamics by elimination of stable modes, the Poincaré surface of section technique and the iteration of maps. Disorder is then interpreted rather as temporal chaos arising from the sensitivity of trajectories to initial conditions and small perturbations.