ItemArticle

Regulation of axisymmetric Rayleigh-Bard convection using boundary temperature coupling of the two circular plates

Title
Regulation of axisymmetric Rayleigh-Bard convection using boundary temperature coupling of the two circular plates
Creator
Kanchana, C.; Siddheshwar, P.G.; Laroze, D.
Description
Controlled delay of regular, chaotic, and periodic regimes of instabilities is studied in the problem of axisymmetric Rayleigh-Bard convection in a vertical cylinder. A feedback control is assumed at the boundaries, which leads to a coupling of the two boundary temperatures. A classical type solution is impossible in such a situation. Hence, a novel series solution procedure is adopted to arrive at the generalized Lorenz model. Due to feedback control, delayed onset of regular convection is observed and the percentage of such a delay as a function of the controller gain parameter, K , is reported. The changes in the pitchfork bifurcation point, the homoclinic orbit, and the Hopf bifurcation point due to feedback control are highlighted with the help of a bifurcation diagram. This diagram shows that the influence of feedback control is to advance the onset of homoclinic bifurcation and delay the onset of Hopf bifurcation. The results indicate that feedback control shows preference for Hopf bifurcation and is antagonistic toward homoclinic bifurcation. The shortening of the time of existence of the strange attractor intermittent with a periodic/quasi-periodic state, which is preceded by the fully periodic motion as K increases is observed using the largest-Lyapunov-exponent plot, the bar-code plot, and the bifurcation diagram. The results coming out of the Kaplan-Yorke dimension reiterates the results depicted by other indicators concerning the influence of K on chaos. The practical importance of the control strategy that is used in the paper is also mentioned in the paper. 2025 Author(s).
Source
Physics of Fluids;Volume;37;Issue;3;Article No.;34129;
Date
01-01-2025
Publisher
American Institute of Physics
Coverage
Kanchana C., Instituto de Alta Investigaci, Universidad de Tarapac Casilla 7 D, Arica, 1000000, Chile; Siddheshwar P.G., Center for Mathematical Needs, Department of Mathematics, CHRIST University, Bengaluru, 560029, India; Laroze D., Instituto de Alta Investigaci, Universidad de Tarapac Casilla 7 D, Arica, 1000000, Chile
Rights
Restricted Access; Hardcopy may be available in the library
Relation
ISSN: 10706631; CODEN: PHFLE
Format
online
Language
English
Type
Article

Citation

Kanchana, C.; Siddheshwar, P.G.; Laroze, D., “Regulation of axisymmetric Rayleigh-Bard convection using boundary temperature coupling of the two circular plates,” CHRIST (Deemed To Be University) Institutional Repository, accessed June 18, 2026, https://archives.christuniversity.in/items/show/22619.

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