ItemArticle

Controlling Chaos in an Axisymmetric RayleighBard Convection in a Cylindrical Enclosure with Variable Gravity Fields

Title
Controlling Chaos in an Axisymmetric RayleighBard Convection in a Cylindrical Enclosure with Variable Gravity Fields
Creator
Arshika, S. Noor; Siddheshwar, P.G.; Tarannum, Sameena; Laroze, D.
Description
The effect of variable gravity fields that vary through the height of a viscous fluid layer in an axisymmetric convection occupying a cylindrical enclosure heated from below is investigated for various radius-to-height ratios. Linear and nonlinear analyses are performed, which makes the present work the first of its kind. A minimal Fourier-series expansion leads to a boundary eigenvalue problem with variable coefficients. Using the Maclaurin-series approach, the recurrence relations for six cases of gravity fields, namely, positively linear, negatively linear, parabolic, cubic, bi-squared, and exponential gravity fields, are generated. The eigenvalue of the problem is located using the NewtonRaphson method with an error tolerance of 10?8 for idealistic and realistic boundary conditions. The scaled-Lorenz model obtained in this paper has newly defined nondimensional parameters that capture the influence of gravity fields and pave the way to examining the dynamical system. The control of chaos for this setup is implemented using various indicators. It is found that the effect of increasing the strength of gravity is to delay the appearance of chaos for all cases of gravity fields except for the positively linear case. Further, by varying the gravity fields, one can witness shifts in the chaotic and periodic regimes. Moreover, the before- and after-effects of going through a periodic regime are examined. In the absence of the gravity variation parameter, the results of the constant-gravity problem are recovered. Ultimately, the rectangular enclosure is studied as a limiting case of the cylindrical enclosure problem. 2026 World Scientific Publishing Company.
Source
International Journal of Bifurcation and Chaos;Volume;36;Issue;9;Article No.;2650121;
Date
01-01-2026
Publisher
World Scientific
Subject
chaos; cylindrical enclosure; dynamical system; NewtonRaphson method; RayleighBard convection; RungeKutta method; variable gravity
Coverage
Arshika S.N., Department of Mathematics, Dayananda Sagar College of Engineering, Kumaraswamy Layout, Bengaluru, 560078, India; Siddheshwar P.G., Centre for Mathematical Needs, Department of Mathematics, Christ University, Hosur Road, Bengaluru, 560029, India; Tarannum S., Department of Professional Studies, Christ University, Hosur Road, Bengaluru, 560029, India; Laroze D., Instituto de Alta Investigaci, Universidad de Tarapac Casilla 7 D, Chile
Rights
Restricted Access; Hardcopy may be available in the library
Relation
ISSN: 2181274;
Format
online
Language
English
Type
Article

Citation

Arshika, S. Noor; Siddheshwar, P.G.; Tarannum, Sameena; Laroze, D., “Controlling Chaos in an Axisymmetric RayleighBard Convection in a Cylindrical Enclosure with Variable Gravity Fields,” CHRIST (Deemed To Be University) Institutional Repository, accessed June 18, 2026, https://archives.christuniversity.in/items/show/23018.

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