Low dimensional models of dynamo action in rotating magnetoconvection

Mondal, Hiya; Das, Alaka; Kumar, Krishna

doi:10.1016/j.chaos.2020.110600

Cited by 1 publication

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“…The effort of constructing low dimensional model has been started since the pioneer work by Lorenz (1963). Low dimensional models (Bhattacharjee and McKane 1988, Das et al 2000, Gunes 2002, Basak 2019, Pal et al 2019, Mondal et al 2021 for RB convection are commonly derived using the Galerkin method. A major point for making finite mode truncation is to take into account whether the model yields qualitatively the same features as there are in the full partial differential equations.…”

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confidence: 99%

Energy-conserving model of hexagonal pattern in Rayleigh-Bénard convection

Mondal¹,

Das²

2022

Fluid Dyn. Res.

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We have constructed an energy-conserving sixteen mode dynamical system to model hexagonal pattern in Rayleigh-Bénard convection of Boussinesq fluids with symmetric stress-free thermally conducting boundaries. The model shows stable roll pattern at the onset of convection. Hexagon is found to appear in the system via sausage and (or) stationary rhombus patterns. Both up and down hexagons arise periodically or chaotically with roll, sausage and rhombus patterns. Hexagonal patterns exist for all values of the Prandtl number, 1 ≤ Pr ≤ 5 explored here. However the pattern is more prominent for small Pr and k < kc , where k denotes the wave number. The plot of Nusselt number matches with previous theoretical result. In dissipationless limit, the total energy and the unavailable energy are constants though the kinetic energy, the potential energy and the available energy vary with time. The derived model does not diverge for large values of Rayleigh number Ra.

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