Browsing by Author "Fischer, P. F."

Now showing 1 - 6 of 6
  • Thumbnail Image
    Extensive chaos in Rayleigh-Benard convection
    Paul, Mark R.; Einarsson, M. I.; Fischer, P. F.; Cross, M. C. (American Physical Society, 2007-04-26)
    Using large-scale numerical calculations we explore spatiotemporal chaos in Rayleigh-Bénard convection for experimentally relevant conditions. We calculate the spectrum of Lyapunov exponents and the Lyapunov dimension describing the chaotic dynamics of the convective fluid layer at constant thermal driving over a range of finite system sizes. Our results reveal that the dynamics of fluid convection is truly chaotic for experimental conditions as illustrated by a positive leading-order Lyapunov exponent. We also find the chaos to be extensive over the range of finite-sized systems investigated as indicated by a linear scaling between the Lyapunov dimension of the chaotic attractor and the system size. © 2007 The American Physical Society.
  • Thumbnail Image
    Large eddy simulation of turbulent channel flows by the rational large eddy simulation model
    Iliescu, Traian; Fischer, P. F. (AIP Publishing, 2003-10)
    The rational large eddy simulation (RLES) model is applied to turbulent channel flows. This approximate deconvolution model is based on a rational (subdiagonal Pade) approximation of the Fourier transform of the Gaussian filter and is proposed as an alternative to the gradient (also known as the nonlinear or tensor-diffusivity) model. We used a spectral element code to perform large eddy simulations of incompressible channel flows at Reynolds numbers based on the friction velocity and the channel half-width Re(tau)=180 and Re(tau)=395. We compared the RLES model with the gradient model and the Smagorinsky model with Van Driest damping. The RLES model was much more stable than the gradient model and yielded improved results. Both the RLES model and the gradient model predicted the off-diagonal Reynolds stresses better than the Smagorinsky model with Van Driest damping. The latter, however, yielded better results for the diagonal Reynolds stresses. (C) 2003 American Institute of Physics.
  • Thumbnail Image
    Pattern formation and dynamics in Rayleigh-Benard convection: Numerical simulations of experimentally realistic geometries
    Paul, Mark R.; Chiam, K. H.; Cross, M. C.; Fischer, P. F.; Greenside, H. S. (Elsevier, 2003-10-01)
    Rayleigh-Bénard convection is studied and quantitative comparisons are made, where possible, between theory and experiment by performing numerical simulations of the Boussinesq equations for a variety of experimentally realistic situations. Rectangular and cylindrical geometries of varying aspect ratios for experimental boundary conditions, including fins and spatial ramps in plate separation, are examined with particular attention paid to the role of the mean flow. A small cylindrical convection layer bounded laterally either by a rigid wall, fin, or a ramp is investigated and our results suggest that the mean flow plays an important role in the observed wavenumber. Analytical results are developed quantifying the mean flow sources, generated by amplitude gradients, and its effect on the pattern wavenumber for a large-aspect-ratio cylinder with a ramped boundary. Numerical results are found to agree well with these analytical predictions. We gain further insight into the role of mean flow in pattern dynamics by employing a novel method of quenching the mean flow numerically. Simulations of a spiral defect chaos state where the mean flow is suddenly quenched is found to remove the time dependence, increase the wavenumber and make the pattern more angular in nature.
  • Thumbnail Image
    Power-law behavior of power spectra in low Prandtl number Rayleigh-Benard convection
    Paul, Mark R.; Cross, M. C.; Fischer, P. F.; Greenside, H. S. (American Physical Society, 2001-09-25)
    The origin of the power-law decay measured in the power spectra of low Prandtl number Rayleigh-Bénard convection near the onset of chaos is addressed using long time numerical simulations of the three-dimensional Boussinesq equations in cylindrical domains. The power law is found to arise from quasidiscontinuous changes in the slope of the time series of the heat transport associated with the nucleation of dislocation pairs and roll pinch-off events. For larger frequencies, the power spectra decay exponentially as expected for time continuous deterministic dynamics.
  • Thumbnail Image
    Rayleigh-Benard convection in large-aspect-ratio domains
    Paul, Mark R.; Chiam, K. H.; Cross, M. C.; Fischer, P. F. (American Physical Society, 2004-08-04)
    The coarsening and wave number selection of striped states growing from random initial conditions are studied in a nonrelaxational, spatially extended, and far-from-equilibrium system by performing large-scale numerical simulations of Rayleigh-Bénard convection in a large-aspect-ratio cylindrical domain with experimentally realistic boundaries. We find evidence that various measures of the coarsening dynamics scale in time with different power-law exponents, indicating that multiple length scales are required in describing the time dependent pattern evolution. The translational correlation length scales with time as t0.12, the orientational correlation length scales as t0.54, and the density of defects scale as t(-0.45). The final pattern evolves toward the wave number where isolated dislocations become motionless, suggesting a possible wave number selection mechanism for large-aspect-ratio convection.
  • Thumbnail Image
    Traveling waves in rotating Rayleigh-Benard convection: Analysis of modes and mean flow
    Scheel, J. D.; Paul, Mark R.; Cross, M. C.; Fischer, P. F. (American Physical Society, 2003-12-31)
    Numerical simulations of the Boussinesq equations with rotation for realistic no-slip boundary conditions and a finite annular domain are presented. These simulations reproduce traveling waves observed experimentally. Traveling waves are studied near threshold by using the complex Ginzburg-Landau equation (CGLE): a mode analysis enables the CGLE coefficients to be determined. The CGLE coefficients are compared with previous experimental and theoretical results. Mean flows are also computed and found to be more significant as the Prandtl number decreases (from sigma=6.4 to sigma=1). In addition, the mean flow around the outer radius of the annulus appears to be correlated with the mean flow around the inner radius.