Intermittency Route to Hyperchaos in 3D Rayleigh-Benard Convection

Abstract:

Convective instabilities of viscous conducting fluids play an important role in many physical phenomena in planets and stars. Astrophysical magnetic fields are usually explained in a framework of the dynamo theory, describing transformation of the kinetic energy of a flow into magnetic energy. Therefore, an analysis of purely convective states and their bifurcations, as a control parameters is changed, provides a detailed framework for the subsequent study of magnetic field generation by these states. In this paper, three-dimensional Rayleigh-Benard convection is investigated numerically for various values of the Rayleigh number and a fixed Prandtl number (corresponding to its value for convection in the Earth’s outer core). On increasing the Rayleigh number, we identify periodic, quasiperiodic, chaotic and hyperchaotic attractors of the convective system and their bifurcations, thereby describing a route to weak turbulence in the convective system.