Rayleigh-Bénard Convection in Large-Aspect-Ratio Domains

Paul, Mark; Kh, Chiam; Mc, Cross; Pf, Fischer

doi:10.1103/physrevlett.93.064503

Cited by 9 publications

(17 citation statements)

References 15 publications

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“…We initially focus our attention on experiments (17) - (19) in Ref. [6] as a representative example of experimental bioconvection.…”

Section: A Comparison With Experimentsmentioning

confidence: 99%

“…Figure 4 includes horizontal lines representing several wavelengths of interest. The experimentally measured value of the wavelength at long-times is represented as the dashed line at λ exp ∞ = 0.70 ± 0.05 where we have used the average value from experiments (17)- (19) in Ref. [6].…”

Section: Fig 3 (Color Online)mentioning

confidence: 99%

“…We exploit the significant progress of computational research on Rayleigh-Bénard convection in large domains (c.f. [18,19]) to perform long-time numerical simulations of bioconvection in large spatially extended domains. We are particularly interested in quantifying the pattern dynamics in the nonlinear regime and its comparison with experimental observations.…”

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confidence: 99%

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Bioconvection in spatially extended domains

Karimi

Paul²

2013

Phys. Rev. E

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We numerically explore gyrotactic bioconvection in large spatially extended domains of finite depth using parameter values from available experiments with the unicellular alga Chlamydomonas nivalis. We numerically integrate the three-dimensional, time-dependent continuum model of Pedley et al. [J. Fluid Mech. 195, 223 (1988)] using a high-order, parallel, spectral-element approach. We explore the long-time nonlinear patterns and dynamics found for layers with an aspect ratio of 10 over a range of Rayleigh numbers. Our results yield the pattern wavelength and pattern dynamics which we compare with available theory and experimental measurement. There is good agreement for the pattern wavelength at short times between numerics, experiment, and a linear stability analysis. At long times we find that the general sequence of patterns given by the nonlinear evolution of the governing equations correspond qualitatively to what has been described experimentally. However, at long times the patterns in numerics grow to larger wavelengths, in contrast to what is observed in experiment where the wavelength is found to decrease with time.

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“…We initially focus our attention on experiments (17) - (19) in Ref. [6] as a representative example of experimental bioconvection.…”

Section: A Comparison With Experimentsmentioning

confidence: 99%

Section: Fig 3 (Color Online)mentioning

confidence: 99%

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confidence: 99%

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Bioconvection in spatially extended domains

Karimi

Paul²

2013

Phys. Rev. E

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“…Experimentally, the use of compressed gases has allowed the construction of shallow convection cells with large lateral extent and fast time scales (de Bruyn et al 1996; 2000). In addition, the underlying fluid dynamical equations (Oberbeck-Boussinesq) are well established and numerical techniques have been developed to simulate systems with many convection rolls (Pesch 1996;Bodenschatz et al 2000;Paul et al 2004).…”

Section: Inclined Layer Convectionmentioning

confidence: 99%

Competition and bistability of ordered undulations and undulation chaos in inclined layer convection

et al. 2008

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Experimental and theoretical investigations of undulation patterns in high-pressure inclined layer gas convection at a Prandtl number near unity are reported. Particular focus is given to the competition between the spatiotemporal chaotic state of undulation chaos and stationary patterns of ordered undulations. In experiments, a competition and bistability between the two states is observed, with ordered undulations most prevalent at higher Rayleigh number. The spectral pattern entropy, spatial correlation lengths and defect statistics are used to characterize the competing states. The experiments are complemented by a theoretical analysis of the Oberbeck–Boussinesq equations. The stability region of the ordered undulations as a function of their wave vectors and the Rayleigh number is obtained with Galerkin techniques. In addition, direct numerical simulations are used to investigate the spatiotemporal dynamics. In the simulations, both ordered undulations and undulation chaos were observed dependent on initial conditions. Experiment and theory are found to agree well

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“…The EMB method was first applied to spiral defect chaos in RBC [46], and has been further used to study that state recently [54,55]. It has also been applied to determine the curvature of RBC coarsening patterns [56,57]. Wavenumber selection in an RBC sample with a radial ramp was studied experimentally [58] using the EMB algorithm, and the ramped system was investigated theoretically [59] using a brute force method to obtain the wavenumber.…”

Section: Introductionmentioning

confidence: 99%

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

Becker

Ahlers

2006

J. Stat. Mech.

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We present new results both from numerical simulations using the Swift-Hohenberg model and from experiment for domain chaos near the onset of rotating Rayleigh-Bénard convection. Using both global Fourier analysis and local wave director (LWD) analysis, the domain chaos patterns were characterized. Several image analysis techniques are discussed and were applied to the director field obtained from LWD analysis. They yielded statistical parameters, averaged over long time series, that characterize several aspects of the chaotic patterns. The effect of the finite image size on the determination of the domain switching frequency obtained with Fourier analysis, as well as with LWD analysis, was investigated. Using the LWD method, we studied ξ θ , a correlation length obtained from the time-averaged autocorrelation of the local angle field θ. The defects and domains in the pattern were examined locally and their average area fraction, average area, and average major axis length were obtained. A periodic component was observed in the time series of the instantaneous correlation lengthξ θ and of the defect area, but was found not to be present in the time series of the domain area. We determined a parameter D, defined as the average dot product of the wave director and the major domain axis, that characterizes the orientation of the domains relative to the roll patterns within them. The results for D were independent of the control parameter ε and of the image size. Simulations and experiment gave remarkably similar results for D.

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Rayleigh-Bénard Convection in Large-Aspect-Ratio Domains

Cited by 9 publications

References 15 publications

Bioconvection in spatially extended domains

Bioconvection in spatially extended domains

Competition and bistability of ordered undulations and undulation chaos in inclined layer convection

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

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