Finite-dimensional description of non-newtonian vortex flows

Abstract
The application of finite-dimensional dynamical systems theory to non-Newtonian vortex flow indicates the presence of complex temporal dynamics that is attributed to shear thinning and normal stress (giving rise to the so-called Weissenberg rod climbing phenomenon). These aspects are examined for Rayleigh-Benard thermal convection and Taylor-Couette rotational flow, in an attempt to elucidate on the mechanisms behind the onset and destabilization of secondary vortex flow common to these and possibly other non-Newtonian flows in the transition regime. Three transition scenarios are particularly explored, namely, the transition to chaos via intermittency, quasiperiodicity and period doubling.