Controlling Chaos in an Axisymmetric Rayleigh–Bénard Convection in a Cylindrical Enclosure with Variable Gravity Fields

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 Newton–Raphson 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.