NONLINEAR-ANALYSIS OF INSTABILITY MODES IN THE TAYLOR-DEAN SYSTEM

The linear and weakly nonlinear stability of flow in the Taylor-Dean s ystem is investigated. The base flow far from the boundaries, is a sup erposition of circular Couette and curved channel Poiseuille flows. Th e computations provide for a finite gap system, critical values of Tay lor numbers, wave numbers and wave speeds for the primary transitions. Moreover, comparisons are made with results obtained in the small gap approximation. It is shown that the occurrence of oscillatory nonaxis ymmetric modes depends on the ''anisotropy'' coefficient in the disper sion relation, and that the critical Taylor number changes slightly wi th the azimuthal wave number for large absolute values of rotation rat io. The weakly nonlinear analysis is made in the framework of the Ginz burg-Landau equations for anisotropic systems. The primary bifurcation towards stationary or traveling rolls is supercritical when Poiseuill e component of the base flow is produced by a partial filling. An exte rnal pumping can induce a subcritical bifurcation for a finite range o f rotation ratio. Special attention is also given to the influence of anisotropy properties on the phase dynamics of bifurcated solution (Ec khaus and Benjamin-Feir conditions).