A numerical investigation of the Schaeffer homotopy in the problem of Taylor‒Couette flows

Numerical methods are used to study the 4, 6-cell exchange process in the Taylor vortex problem, with particular reference to the homotopy devised by Schaeffer. The homotopy describes a transformation between two models, one incorporating periodic boundary conditions and so referring to flows in an infinite annulus, the other with realistic boundary conditions. Our calculations indicate that the former model is more complicated than previously suspected and lead to a better understanding of the consequences of Schaeffer’s device.