Route to hyperchaos in Rayleigh-Benard convection

TL;DR

This paper investigates the transition to hyperchaos in Rayleigh-Benard convection through numerical simulations, revealing a route involving quasiperiodic regimes, multistability, and crises, with Lyapunov exponents indicating weak turbulence.

Contribution

It presents a detailed numerical study of the route to hyperchaos in Rayleigh-Benard convection, identifying specific bifurcations and scaling laws of Lyapunov exponents.

Findings

Identification of a route to hyperchaos involving quasiperiodic regimes.

Linear scaling of Lyapunov exponents with Rayleigh number.

Evidence of weak turbulence in the hyperchaotic regime.

Abstract

Transition to hyperchaotic regimes in Rayleigh-Benard convection in a square periodicity cell is studied by three-dimensional numerical simulations. By fixing the Prandtl number at P=0.3 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.