ON THE EXPLICIT SYMMETRY-BREAKING IN THE TAYLOR-COUETTE PROBLEM

We consider an infinitely long Taylor-Couette problem which is translationally and reflectionally symmetric along the cylinders. We investigate the bifurcation to Taylor vortices when the reflection symmetry in the axial direction is broken in two ways: (i) by applying a constant pressure gradient in the axial direction, (ii) by sliding cylinders relative to each other. We calculate the effect of these symmetry breaking perturbations and find in both cases a slow drifting of the Taylor vortices along the axial direction. We discuss a total symmetry breaking of the translational and reflectional symmetry along the axial direction. This forces the system either to choose a state from a circle of states of the unperturbed system or into an inhomogeneous drifting state.