Finite-dimensional Description of Non-newtonian Vortex Flows

The application of nite-dimensional dynamical systems theory to non-Newtonian vortex ow 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 ow, in an attempt to elucidate on the mechanisms behind the onset and destabilization of secondary vortex ow common to these and possibly other non-Newtonian ows in the transition regime. Three transition scenarios are particularly explored, namely, the transition to chaos via intermittency, quasiperiodicity and period doubling.