Complex dynamics in a short Taylor-Couette annulus

Juan Lopez

Department of Mathematics
Arizona State University

Abstract:

The nonlinear dynamics of the flow in a short annulus driven by the
rotation of the inner cylinder and bottom endwall is considered. The
shortness of the annulus enhances the role of mode competition, and the
associated dynamics are found to be organized by a number of local
codimension-2 bifurcations as well as global homoclinic and heteroclinic
bifurcations. The dynamics are explored using a three-dimensional
Navier-Stokes solver, which is also implemented in a number of invariant
subspaces in order to follow some unstable solution branches and obtain a
fairly complete bifurcation diagram of the mode competitions.