Local wave director analysis of domain chaos in Rayleigh–Bénard convection

Becker, Nathan; Ahlers, Guenter

doi:10.1088/1742-5468/2006/12/p12002

Cited by 5 publications

(1 citation statement)

References 83 publications

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“…The values for L were chosen to be commensurable with the stripes' wavelength λ ≈ 9.4, but a small mismatch as well as global rotation of the system have no significant influence on the results presented below. The local stripe orientation θ (r,t), commonly used to investigate the physics of stripe patterns [15,16,53], was computed using the gradient-square tensor implemented in reciprocal space [54].…”

Section: Model and Methodsmentioning

confidence: 99%

Aging of orientation fluctuations in stripe phases

2014

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Stripe patterns, observed in a large variety of physical systems, often exhibit a slow nonequilibrium dynamics because ordering is impeded by the presence of topological defects. Using computer simulations based on a well-established model for stripe formation, we show that a slow dynamics and aging occur also in stripe patterns free of topological defects. For a wide range of noise strengths, the two-time orientation correlation function follows a scaling form that is typical for systems exhibiting a growing length scale. In our case, the underlying mechanism is the coarsening of orientation fluctuations, ultimately leading to power-law spatial correlations perpendicular to the stripes. Our results show that even for the smallest amount of noise, stripe phases without topological defects do not reach equilibrium. This constitutes an important aspect of the dynamics of modulated phases.

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Section: Model and Methodsmentioning

confidence: 99%

Aging of orientation fluctuations in stripe phases

2014

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Onset of Küppers–Lortz-like dynamics in finite rotating thermal convection

2010

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The onset of thermal convection in a finite rotating cylinder is investigated using direct numerical simulations of the Navier–Stokes equations with the Boussinesq approximation in a regime in which spatio-temporal complexity is observed directly after onset. The system is examined in the non-physical limit of zero centrifugal force as well as with an experimentally realizable centrifugal force, leading to two different paths to Küppers–Lortz-like spatio-temporal chaos. In the idealized case, neglecting centrifugal force, the onset of convection occurs directly from a conduction state, resulting in square patterns with slow roll switching, followed at higher thermal driving by straight roll patterns with faster roll switching. The case with a centrifugal force typical of laboratory experiments exhibits target patterns near the theoretically predicted onset of convection, followed by a rotating wave that emerges via a Hopf bifurcation. A subsequent Hopf bifurcation leads to ratcheting states with sixfold symmetry near the axis. With increasing thermal driving, roll switching is observed within the ratcheting lattice before Küppers–Lortz-like spatio-temporal chaos is observed with the dissolution of the lattice at a slightly stronger thermal driving. For both cases, all of these states are observed within a 2% variation in the thermal driving.

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Correlations between the leading Lyapunov vector and pattern defects for chaotic Rayleigh-Bénard convection

Levanger

Cyranka

et al. 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We probe the effectiveness of using topological defects to characterize the leading Lyapunov vector for a high-dimensional chaotic convective flow field. This is accomplished using large-scale parallel numerical simulations of Rayleigh–Bénard convection for experimentally accessible conditions. We quantify the statistical correlations between the spatiotemporal dynamics of the leading Lyapunov vector and different measures of the flow field pattern’s topology and dynamics. We use a range of pattern diagnostics to describe the flow field structures which includes many of the traditional diagnostics used to describe convection as well as some diagnostics tailored to capture the dynamics of the patterns. We use the ideas of precision and recall to build a statistical description of each pattern diagnostic’s ability to describe the spatial variation of the leading Lyapunov vector. The precision of a diagnostic indicates the probability that it will locate a region where the Lyapunov vector is larger than a threshold value. The recall of a diagnostic indicates its ability to locate all of the possible spatial regions where the Lyapunov vector is above threshold. By varying the threshold used for the Lyapunov vector magnitude, we generate precision-recall curves which we use to quantify the complex relationship between the pattern diagnostics and the spatiotemporally varying magnitude of the leading Lyapunov vector. We find that pattern diagnostics which include information regarding the flow history outperform pattern diagnostics that do not. In particular, an emerging target defect has the highest precision of all of the pattern diagnostics we have explored.

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Local wave director analysis of domain chaos in Rayleigh–Bénard convection

Cited by 5 publications

References 83 publications

Aging of orientation fluctuations in stripe phases

Aging of orientation fluctuations in stripe phases

Onset of Küppers–Lortz-like dynamics in finite rotating thermal convection

Correlations between the leading Lyapunov vector and pattern defects for chaotic Rayleigh-Bénard convection

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