Influence of Coriolis force on the emergence of chaos in a generalized Lorenz model of a buoyancy-driven convective system

Abstract

The influence of Coriolis force on the stability of a uniformly rotating Rayleigh–Bénard system is investigated using a generalized five-dimensional Lorenz model. The study uncovers several new dynamical features, notably due to the inclusion of a horizontal velocity mode that is independent of the vertical coordinate, leading to qualitatively different rotational effects not captured by previous models. A comparative analysis with an extended Lorenz model representing a magnetoconvective system reveals a striking parallel: the rotation rate, akin to the magnetic field strength in magnetoconvection, delays the onset of chaos and favors periodicity from steady convection. Numerical estimations of the Hopf–Rayleigh number show that an increase in the scaled Taylor number – quantifying the rotation rate – shifts the Hopf bifurcation to a higher temperature gradient, indicating enhanced stabilization. The appearance of a strange attractor, signified by the emergence of chaos, is examined using bifurcation diagrams, largest Lyapunov exponent plots, and three-dimensional projections of the five-dimensional phase space trajectories. Notably, at high rotation rates, the system undergoes a well-defined period-doubling transition to chaos consistent with Feigenbaum universality, following the onset of periodic convection directly from the steady state – a phenomenon previously unreported in the context of rotating convection. These results establish rotation as a viable control mechanism for chaos in convective systems and underscore a deeper universality between Coriolis and Lorentz forces in regulating nonlinear thermal instabilities.