Journal of Fluid Mechanics


Onset of Küppers–Lortz-like dynamics in finite rotating thermal convection

A. RUBIOa1, J. M. LOPEZa1 c1 and F. MARQUESa2

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)

Key Words:

  • Convection;
  • Rotating flows;
  • Pattern formation


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