Quantifying Spatiotemporal Chaos in Rayleigh-Bénard Convection

Abstract

Using large-scale parallel numerical simulations we explore spatiotemporal chaos in Rayleigh-Bénard convection in a cylindrical domain with experimentally relevant boundary conditions. We use the variation of the spectrum of Lyapunov exponents and the leading order Lyapunov vector with system parameters to quantify states of high-dimensional chaos in fluid convection. We explore the relationship between the time dynamics of the spectrum of Lyapunov exponents and the pattern dynamics. For chaotic dynamics we find that all of the Lyapunov exponents are positively correlated with the leading order Lyapunov exponent and we quantify the details of their response to the dynamics of defects. The leading order Lyapunov vector is used to identify topological features of the fluid patterns that contribute significantly to the chaotic dynamics. Our results show a transition from boundary dominated dynamics to bulk dominated dynamics as the system size is increased. The spectrum of Lyapunov exponents is used to compute the variation of the fractal dimension with system parameters to quantify how the underlying high-dimensional strange attractor accommodates a range of different chaotic dynamics.

References in corpus (4)

• Large scale dynamics in turbulent Rayleigh-Benard convection
• Characterizing dynamics with covariant Lyapunov vectors
• Extensive Chaos in the Lorenz-96 Model
• Structure of characteristic Lyapunov vectors in spatiotemporal chaos

Cited by in corpus (6)

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• Route to hyperchaos in Rayleigh-Benard convection
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• Dissipative structures in a parametrically driven dissipative lattice: chimera, localized disorder, continuous-wave, and staggered state
• Spiral defect chaos in Rayleigh-Bénard convection: Asymptotic and numerical studies of azimuthal flows induced by rotating spirals