Competition of Azimuthal Modes and Quasi-Periodic Flows in the Couette-Taylor Problem

Abstract

The classical Couette Taylor experiment consists in looking at the flow of a viscous fluid between two coaxial cylinders which rotate at constant (but independent) speeds. The speed of rotation of the inner cylinder is responsible for the destabilization mechanism of the basic laminar flow (called the Couette flow). The great variety of possible regimes before turbulence [1] and the relative simplicity of the model (related to its symmetries), make this problem a very interesting one for the study of transition to turbulence, and also for testing techniques of computation of flows and their stability. After the classical work of G.I. Taylor in the twenties [17] and the introduction of bifurcation techniques by Kirchgasner and Sorger in the sixties [12], progress has been done recently by introducing bifurcation with symmetry and Centre manifold techniques. Using group theoretic methods, Golubitsky and Stewart have classified the possible time-periodic flows which occur from the interaction of an axisym metric disturbance of the Couette flow with a non-axisymmetric one [9].