TY - JOUR
T1 - Pattern formation and dynamics in Rayleigh-Bénard convection
T2 - Numerical simulations of experimentally realistic geometries
AU - Paul, M. R.
AU - Chiam, K. H.
AU - Cross, M. C.
AU - Fischer, P. F.
AU - Greenside, H. S.
N1 - Funding Information:
We are grateful to G. Ahlers for helpful discussions. This research was supported by the US Department of Energy, Grant DE-FT02-98ER14892, and the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, US Department of Energy, under Contract W-31-109-Eng-38. We also acknowledge the Caltech Center for Advanced Computing Research and the North Carolina Supercomputing Center.
PY - 2003/10/1
Y1 - 2003/10/1
N2 - Rayleigh-Bénard convection is studied and quantitative comparisons are made, where possible, between theory and experiment by performing numerical simulations of the Boussinesq equations for a variety of experimentally realistic situations. Rectangular and cylindrical geometries of varying aspect ratios for experimental boundary conditions, including fins and spatial ramps in plate separation, are examined with particular attention paid to the role of the mean flow. A small cylindrical convection layer bounded laterally either by a rigid wall, fin, or a ramp is investigated and our results suggest that the mean flow plays an important role in the observed wavenumber. Analytical results are developed quantifying the mean flow sources, generated by amplitude gradients, and its effect on the pattern wavenumber for a large-aspect-ratio cylinder with a ramped boundary. Numerical results are found to agree well with these analytical predictions. We gain further insight into the role of mean flow in pattern dynamics by employing a novel method of quenching the mean flow numerically. Simulations of a spiral defect chaos state where the mean flow is suddenly quenched is found to remove the time dependence, increase the wavenumber and make the pattern more angular in nature. Published by Elsevier B.V.
AB - Rayleigh-Bénard convection is studied and quantitative comparisons are made, where possible, between theory and experiment by performing numerical simulations of the Boussinesq equations for a variety of experimentally realistic situations. Rectangular and cylindrical geometries of varying aspect ratios for experimental boundary conditions, including fins and spatial ramps in plate separation, are examined with particular attention paid to the role of the mean flow. A small cylindrical convection layer bounded laterally either by a rigid wall, fin, or a ramp is investigated and our results suggest that the mean flow plays an important role in the observed wavenumber. Analytical results are developed quantifying the mean flow sources, generated by amplitude gradients, and its effect on the pattern wavenumber for a large-aspect-ratio cylinder with a ramped boundary. Numerical results are found to agree well with these analytical predictions. We gain further insight into the role of mean flow in pattern dynamics by employing a novel method of quenching the mean flow numerically. Simulations of a spiral defect chaos state where the mean flow is suddenly quenched is found to remove the time dependence, increase the wavenumber and make the pattern more angular in nature. Published by Elsevier B.V.
KW - Boussinesq equations
KW - Nonequilibrium systems
KW - Rayleigh-Bénard convection
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U2 - 10.1016/S0167-2789(03)00216-1
DO - 10.1016/S0167-2789(03)00216-1
M3 - Article
AN - SCOPUS:0141865723
SN - 0167-2789
VL - 184
SP - 114
EP - 126
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 1-4
ER -