a1 Department of Mathematics and Statistics, Arizona State University, Tempe AZ 85287, USA
a2 Departament de Física Aplicada, Universitat Politècnica de Catalunya, Barcelona 08034, Spain
The onset of thermal convection in a finite rotating cylinder is investigated using direct numerical simulations of the Navier–Stokes equations with the Boussinesq approximation in a regime in which spatio-temporal complexity is observed directly after onset. The system is examined in the non-physical limit of zero centrifugal force as well as with an experimentally realizable centrifugal force, leading to two different paths to Küppers–Lortz-like spatio-temporal chaos. In the idealized case, neglecting centrifugal force, the onset of convection occurs directly from a conduction state, resulting in square patterns with slow roll switching, followed at higher thermal driving by straight roll patterns with faster roll switching. The case with a centrifugal force typical of laboratory experiments exhibits target patterns near the theoretically predicted onset of convection, followed by a rotating wave that emerges via a Hopf bifurcation. A subsequent Hopf bifurcation leads to ratcheting states with sixfold symmetry near the axis. With increasing thermal driving, roll switching is observed within the ratcheting lattice before Küppers–Lortz-like spatio-temporal chaos is observed with the dissolution of the lattice at a slightly stronger thermal driving. For both cases, all of these states are observed within a 2% variation in the thermal driving.
(Received June 04 2009)
(Revised September 22 2009)
(Accepted September 22 2009)