Route to hyperchaos in Rayleigh-Bénard convection
1 Aeronautics Institute of Technology - São José dos Campos, São Paulo 12228-900, Brazil
2 National Institute for Space Research and World Institute for Space Environment Research P.O. Box 515, São José dos Campos, São Paulo 12227-010, Brazil
Received: 1 June 2015
Accepted: 24 September 2015
Transition to hyperchaotic regimes in Rayleigh-Bénard convection in a square periodicity cell is studied by three-dimensional numerical simulations. By fixing the Prandtl number at and varying the Rayleigh number as a control parameter, a bifurcation diagram is constructed where a route to hyperchaos involving quasiperiodic regimes with two and three incommensurate frequencies, multistability, chaotic intermittent attractors and a sequence of boundary and interior crises is shown. The three largest Lyapunov exponents exhibit a linear scaling with the Rayleigh number and are positive in the final hyperchaotic attractor. Thus, a route to weak turbulence is found.
PACS: 47.52.+j – Chaos in fluid dynamics / 47.20.Bp – Buoyancy-driven instabilities (e.g., Rayleigh-Benard) / 47.27.ed – Dynamical systems approaches
© EPLA, 2015