Boundary-layer and interior separations in the Taylor–Couette–Poiseuille flow

Abstract

In this article, we derive a rigorous characterization of the boundary-layer and interior separations in the Taylor–Couette–Poiseuille flow. The results obtained provide a rigorous characterization on how, when, and where the propagating Taylor vortices (PTVs) are generated. We consider only the narrow gap and axisymmetric case where a pressure gradient is applied along the axis where the cylinders rotate and where there are no radial motions. In this case, the governing equations are an approximation of the classical Bénard equations. In particular, contrary to what is commonly believed, in the case under consideration, we show that the PTVs do not appear after the first dynamical bifurcation, and they appear only when the Taylor number is further increased to cross another critical value so that a structural bifurcation occurs. This structural bifurcation corresponds to the boundary-layer and interior separations of the flow structure in the physical space.