Convective Instabilities and Low Dimensional Modeling

Pal, Pinaki; Ghosh, Manojit; Banerjee, Ankan; Ghosh, Paromita; Nandukumar, Yada; Sharma, Lekha

doi:10.1007/978-981-15-0536-2_17

Cited by 2 publications

(1 citation statement)

References 36 publications

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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.…”

Section: Introductionmentioning

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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Section: Introductionmentioning

confidence: 99%

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

Mondal¹,

Das²

2022

Fluid Dyn. Res.

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Supercritical and subcritical rotating convection in a horizontally periodic box with no-slip walls at the top and bottom

et al. 2022

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The study of instabilities in the convection of rotating fluids is one of the classical topics of research. However, in spite of more than five decades of research, the instabilities and related transition scenario near the onset of rotating convection of low Prandtl number fluids is not well understood. Here we investigate the transition scenario in rotating Rayleigh-B\'{e}nard convection with no slip boundary conditions by performing 3D direct numerical simulations (DNS) and low dimensional modeling. The governing parameters, namely, the Taylor number ($\mathrm{Ta}$), Rayleigh number ($\mathrm{Ra}$) and Prandtl number ($\mathrm{Pr}$) are varied in the ranges $0< \mathrm{Ta}\leq 8\times 10^3$, $0 <\mathrm{Ra} < 1\times 10^4$ and $0 <\mathrm{Pr} \leq 0.35$, where convection appears as stationary cellular pattern. In DNS, for $\mathrm{Pr} < 0.31$, supercritical or subcritical onset of convection appears, according as $\mathrm{Ta} > \mathrm{Ta_c}(\mathrm{Pr})$ or $\mathrm{Ta} < \mathrm{Ta_c}(\mathrm{Pr})$, where $\mathrm{Ta_c}(\mathrm{Pr})$ is a $\mathrm{Pr}$ dependent threshold of $\mathrm{Ta}$. On the other hand, only supercritical onset of convection is observed for $\mathrm{Pr}\geq 0.31$. At the subcritical onset, both finite amplitude stationary and time dependent solutions are manifested. The origin of these solutions are explained using a low dimensional model. DNS show that as $\mathrm{Ra}$ is increased beyond the onset of convection, the system becomes time dependent and depending on $\mathrm{Pr}$, standing and traveling wave solutions are observed. For very small $\mathrm{Pr}$ ($\leq 0.045$), interestingly, finite amplitude time dependent solutions are manifested at the onset for higher $\mathrm{Ta}$.

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Convective Instabilities and Low Dimensional Modeling

Cited by 2 publications

References 36 publications

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

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

Supercritical and subcritical rotating convection in a horizontally periodic box with no-slip walls at the top and bottom

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