TY - JOUR
T1 - Onset of Kppers-Lortz-like dynamics in finite rotating thermal convection
AU - Rubio, A.
AU - Lopez, Juan
AU - Marques, F.
N1 - Funding Information:
This work was supported in part by the US National Science Foundation grant DMS-0509594, the Spanish and Catalan government grants FIS2007-61585 and SGR-00024 and the Korean Science and Engineering Foundation WCU grant R32-2009-000-20021-0. Rubio was supported by a Fulbright fellowship at UPC (Barcelona, Spain), whose hospitality is warmly appreciated. Computations were performed using the ASU Fulton High Performance Computing Initiative and the Ranger cluster using the NSF Teragrid grant TG-DMS090029. Supplementary movies available at journals.cambridge.org/flm.
PY - 2010/2/10
Y1 - 2010/2/10
N2 - 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 Kppers-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 Kppers-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.
AB - 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 Kppers-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 Kppers-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.
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U2 - 10.1017/S0022112009992400
DO - 10.1017/S0022112009992400
M3 - Article
AN - SCOPUS:77952431205
SN - 0022-1120
VL - 644
SP - 337
EP - 357
JO - journal of fluid mechanics
JF - journal of fluid mechanics
ER -