An incompressible liquid flow in the gap between two coaxial cylinders, such that the inner rotating (wavy) cylinder has a periodically varying radius along the axial direction while the outer stationary cylinder has a constant radius, is studied experimentally and theoretically. Basic attention is focused on the symmetry-breaking phenomenon of the vortex flow arising from the rotation of the inner wavy cylinder. It is found that the symmetry-breaking phenomenon of the vortical flow structures in this geometry is accompanied by the occurrence of a self-induced axial pressure gradient. A theoretical formulation of the problem of periodic vortical flow prevailing in such a geometry having large axial length is presented. The comparison between the computed and the experimental results is presented and the underlying phenomena are discussed. PUBLICATION ABSTRACT