Study of chaos in the Darcy-Bard convection problem with Robin boundary condition on the upper surface

Title

Study of chaos in the Darcy-Bard convection problem with Robin boundary condition on the upper surface

Creator

Siddheshwar P.G.; Soibam D.D.; Laroze D.

Description

Possibility of chaos is studied in Darcy-Bard convection using the Dirichlet and the Robin boundary condition at the lower and upper boundaries, respectively. Comparison is made with the results of Dirichlet (classical-Darcy-Bard convection, CDBC) and Neumann boundary condition (Barletta-Darcy-Bard convection, BDBC). It is found that the cell size at onset is bigger in the case of BDBC compared to the generalized-Darcy-Bard convection (GDBC) and much bigger compared to CDBC. The critical-Darcy-Rayleigh number of BDBC is found to be the least and that of CDBC is the largest. Nonlinear-stability-analysis is performed leading to the scaled-generalized-Vadasz-Lorenz model (SGVLM). In deriving this model, help is sought from a local-nonlinear-stability-analysis that yields the form of the convective-mode. The SGVLM is shown to be dissipative and conservative, with its bounded solution trapped within an ellipsoid. Onset of chaos and its characteristics are studied using the Hopf-Rayleigh-number, the Lorenz-butterfly-diagram, and the plot of the amplitude of the convective-mode vs the control-parameter, R, which is the eigenvalue. Chaos sets in earlier in CDBC and much later in BDBC when compared to that in GDBC. Beyond the onset of chaos is seen a sequence of chaotic and periodic motions, with the latter sometimes being present for an extended period. 2024 Author(s).

Source

Physics of Fluids, Vol-36, No. 1

Date

2024-01-01

Publisher

American Institute of Physics Inc.

Coverage

Siddheshwar P.G., Centre for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, 560029, India; Soibam D.D., Centre for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, 560029, India; Laroze D., Instituto de Alta Investigaci, Universidad de Tarapac Casilla 7 D, Arica, Chile

Rights

All Open Access; Bronze Open Access

Relation

ISSN: 10706631; CODEN: PHFLE

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.1063/5.0180488

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