Nonlinear Dynamics

, Volume 94, Issue 4, pp 2763–2784 | Cite as

Study of a periodically forced magnetohydrodynamic system using Floquet analysis and nonlinear Galerkin modelling

  • Arnab Basak
Original Paper


We present a detailed study of Rayleigh–Bénard magnetoconvection with periodic gravity modulation and uniform vertical magnetic field. Linear stability analysis is carried out using Floquet theory to construct the stability boundaries in order to estimate the magnitude of forcing amplitude \(\epsilon \) required for having convection in the system for a fixed Rayleigh number Ra, wave number k and modulating frequency \(\Omega \). The effects of varying Prandtl number Pr and Chandrasekhar number Q on the threshold of convection are also investigated. A higher Pr value reduces the value of the threshold, whereas a higher Q value increases it. Bicritical states are also observed at which the minimum forcing amplitude needed for convection to begin occurs at two different k values in harmonic and sub-harmonic regions, respectively. We also construct a nonlinear Galerkin model and compare the results with those obtained from linear stability analysis. Two-dimensional (2D) oscillatory convection is observed at the onset, while quasiperiodic and chaotic behaviours are found at higher Ra values. 2D as well as nonlinear convective flow patterns are observed for primary and higher-order instabilities, respectively. Bifurcation diagrams with respect to different parameters such as \(\epsilon \), Ra and Q are provided for thorough understanding of the forced nonlinear system.


Driven magnetoconvection Modelling Bifurcations 



I acknowledge the financial support from the Center of Excellence in Space Sciences India (CESSI) funded by the Ministry of Human Resource Development, Government of India. I am grateful to my Ph.D. supervisor Prof. Krishna Kumar for learning different numerical techniques from him and to my father Tushar Kanti Basak for fruitful discussions. I am obliged to the anonymous referees whose valuable suggestions have helped improve the standard of the paper.

Disclosure Of Potential Conflicts Of Interest


The study was funded by the Ministry of Human Resource Development, Government of India via the Center of Excellence in Space Sciences India (CESSI).

Conflict of interest

The author declares that there is no conflict of interest.


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Authors and Affiliations

  1. 1.Center of Excellence in Space Sciences IndiaIndian Institute of Science Education and Research KolkataMohanpurIndia

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