To describe the pattern formation just above the first instability of the rotating Couette-Taylor system in the presence of an externally imposed axial through-flow, an amplitude equation has been derived for the case of a stationary outer cylinder. All linear and nonlinear coefficients of this complex Ginzburg-Landau equation have been calculated numerically and are expressed for a wide range of radius ratios as a function of through-flow strength for small Reynolds numbers. A shooting method has been used to obtain the critical properties of the system. Also, the boundary of the convectively unstable regime has been determined.

• Received 30 July 1993

DOI:https://doi.org/10.1103/PhysRevE.48.4444