arXiv subjects

H. S. Greenside

Publications and source records attributed to H. S. Greenside.

7 recordsLinked to original sources

arXiv2004

Enhanced tracer transport by the spiral defect chaos state of a convecting fluid

To understand how spatiotemporal chaos may modify material transport, we use direct numerical simulations of the three-dimensional Boussinesq equations and of an advection-diffusion equation to study the transport of a passive tracer by the spiral defect chaos state of a convecting fluid. The simulations show that the transport is diffusive and is enhanced by the spatiotemporal chaos. The enhancement in tracer diffusivity follows two regimes. For large Peclet numbers (that is, small molecular diffusivities of the tracer), we find that the enhancement is proportional to the Peclet number. For small Peclet numbers, the enhancement is proportional to the square root of the Peclet number. We explain the presence of these two regimes in terms of how the local transport depends on the local wave numbers of the convection rolls. For large Peclet numbers, we further find that defects cause the tracer diffusivity to be enhanced locally in the direction orthogonal to the local wave vector but suppressed in the direction of the local wave vector.

nlin.PS↗

arXiv2003

Efficient Algorithm on a Non-staggered Mesh for Simulating Rayleigh-Benard Convection in a Box

An efficient semi-implicit second-order-accurate finite-difference method is described for studying incompressible Rayleigh-Benard convection in a box, with sidewalls that are periodic, thermally insulated, or thermally conducting. Operator-splitting and a projection method reduce the algorithm at each time step to the solution of four Helmholtz equations and one Poisson equation, and these are are solved by fast direct methods. The method is numerically stable even though all field values are placed on a single non-staggered mesh commensurate with the boundaries. The efficiency and accuracy of the method are characterized for several representative convection problems.

nlin.PS↗

arXiv2002

Mean flow and spiral defect chaos in Rayleigh-Benard convection

We describe a numerical procedure to construct a modified velocity field that does not have any mean flow. Using this procedure, we present two results. Firstly, we show that, in the absence of mean flow, spiral defect chaos collapses to a stationary pattern comprising textures of stripes with angular bends. The quenched patterns are characterized by mean wavenumbers that approach those uniquely selected by focus-type singularities, which, in the absence of mean flow, lie at the zig-zag instability boundary. The quenched patterns also have larger correlation lengths and are comprised of rolls with less curvature. Secondly, we describe how mean flow can contribute to the commonly observed phenomenon of rolls terminating perpendicularly into lateral walls. We show that, in the absence of mean flow, rolls begin to terminate into lateral walls at an oblique angle. This obliqueness increases with Rayleigh number.

nlin.PS↗

arXiv2002

Pattern Formation and Dynamics in Rayleigh-Bénard Convection: Numerical Simulations of Experimentally Realistic Geometries

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.

nlin.PS↗

arXiv2001

Power-Law Behavior of Power Spectra in Low Prandtl Number Rayleigh-Benard Convection

The origin of the power-law decay measured in the power spectra of low Prandtl number Rayleigh-Benard 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 quasi-discontinuous 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.

nlin.PS↗

arXiv2000

Simulating Complex Dynamics In Intermediate And Large-Aspect-Ratio Convection Systems

Buoyancy-induced (Rayleigh-Benard) convection of a fluid between two horizontal plates is a central paradigm for studying the transition to complex spatiotemporal dynamics in sustained nonequilibrium systems. To improve the analysis of experimental data and the quantitative comparison of theory with experiment, we have developed a three-dimensional finite-difference code that can integrate the three-dimensional Boussinesq equations (which govern the evolution of the temperature, velocity, and pressure fields associated with a convecting flow) efficiently in large box-shaped domains with experimentally appropriate lateral boundary conditions. We discuss some details of this code and present two applications, one to the occurrence of quasiperiodic dynamics with as many as 5 incommensurate frequencies in a moderate-aspect-ratio 10x5 convection cell, and one to the onset of spiral defect chaos in square cells with aspect ratios varying from Gamma=16 to 56.

nlin.PS↗

arXiv1993

A quantitative measurement of spatial order in ventricular fibrillation

As an objective measurement of spatial order in ventricular fibrillation (VF), spatial correlation functions and their characteristic lengths were estimated from epicardial electrograms of pigs in VF. The correlation length of the VF in pigs was found to be approximately 4-10 mm, varying as fibrillation progressed. The degree of correlation decreased in the first 4 seconds after fibrillation then increased over the next minute. The correlation length is much smaller than the scale of the heart, suggesting that many independent regions of activity exist on the epicardium at any one time. On the other hand, the correlation length is 4 to 10 times the interelectrode spacing, indicating that some coherence is present. These results imply that the heart behaves during VF as a high-dimensional, but not random, system involving many spatial degrees of freedom, which may explain the lack of convergence of fractal dimension estimates reported in the literature. Changes in the correlation length also suggest that VF reorganizes slightly in the first minute after an initial breakdown in structure.

patt-sol↗