arXiv subjects

J. D. Gunton

Publications and source records attributed to J. D. Gunton.

24 records · Page 2Linked to original sources

arXiv1997

Direct Transition to Spatiotemporal Chaos in Low Prandtl Number Fluids

We present the first large scale numerical simulation of three-dimensional Rayleigh-Bénard convection near onset, under free-free boundary conditions for a fluid of Prandtl number $σ=0.5$. We find that a spatiotemporally chaotic state emerges immediately above onset, which we investigate as a function of the reduced control parameter $ε$. We conclude that the transition from conduction to spatiotemporal chaos is second order and of ``mean field'' character. We also present a simple theory for the time-averaged convective current. Finally, we show that the time-averaged structure factor satisfies a scaling behavior with respect to the correlation length near onset.

patt-sol↗

arXiv1996

Dynamical Properties of Multi-Armed Global Spirals in Rayleigh-Benard Convection

Explicit formulas for the rotation frequency and the long-wavenumber diffusion coefficients of global spirals with $m$ arms in Rayleigh-Benard convection are obtained. Global spirals and parallel rolls share exactly the same Eckhaus, zigzag and skewed-varicose instability boundaries. Global spirals seem not to have a characteristic frequency $ω_m$ or a typical size $R_m$, but their product $ω_m R_m$ is a constant under given experimental conditions. The ratio $R_i/R_j$ of the radii of any two dislocations ($R_i$, $R_j$) inside a multi-armed spiral is also predicted to be constant. Some of these results have been tested by our numerical work.

patt-sol↗

arXiv1993

Spiral defect chaos in a model of Rayleigh-Benard convection

A numerical solution of a generalized Swift-Hohenberg equation in two dimensions reveals the existence of a spatio-temporal chaotic state comprised of a large number of rotating spirals. This state is observed for a reduced Rayleigh number $ε=0.25$. The power spectrum of the state is isotropic, and the spatial correlation function decays exponentially, with an estimated decay length $ξ\approx 2.5 λ_{c}$, where $λ_{c}$ is the critical wavelength near the onset of convection. Our study suggests that this spiral defect state occurs for low Prandtl numbers and large aspect ratios.

patt-sol↗

arXiv1993

Pattern formation during Rayleigh-Bénard convection in non-Boussinesq fluids

Motivated by recent experimental studies of Bodenschatz et al. [E. Bodenschatz, J.R. de Bruyn, G. Ahlers and D.S. Cannell, Phys. Rev. Lett. {\bf 67}, 3078 (1991) ], we present a numerical study of a generalized two dimensional Swift-Hohenberg equation to model pattern formation in Rayleigh-Bénard convection in a non-Boussinesq fluid. It is shown that many of the features observed in these experiments can be reproduced by this generalized model that explicitly includes non-Boussinesq and mean flow effects. The spontaneous formation of hexagons, rolls, and a rotating spiral pattern is studied, as well as the transitions and competition among them. Mean flow, non-Boussinesq effects, the geometric shape of the lateral wall, and sidewall forcing are all shown to be crucial in the formation of the rotating spirals. We also study nucleation and growth of hexagonal patterns and find that the front velocity in this two dimensional model is consistent with the prediction of marginal stability theory for one dimensional fronts.

patt-sol↗

arXiv1992

Study of spiral pattern formation in Rayleigh-Benard convection

We present a numerical study of a generalized two-dimensional Swift-Hohenberg model of spiral pattern formation in Rayleigh-Bénard convection in a non-Boussinesq fluid. We demonstrate for the first time that a model for convective motion is able to predict in considerable dynamical detail the spontaneous formation of a rotating spiral state from an ordered hexagon state. Our results are in good agreement with recent experimental studies of $CO_{2}$ gas. The mean flow and non-Boussinesq effects are shown to be crucial in forming rotating spirals.

cond-mat↗

arXiv1992

Numerical study of pattern formation following a convective instability in non-Boussinesq fluids

We present a numerical study of a model of pattern formation following a convective instability in a non-Boussinesq fluid. It is shown that many of the features observed in convection experiments conducted on $CO_{2}$ gas can be reproduced by using a generalized two-dimensional Swift-Hohenberg equation. The formation of hexagonal patterns, rolls and spirals is studied, as well as the transitions and competition among them. We also study nucleation and growth of hexagonal patterns and find that the front velocity in this two dimensional model is consistent with the prediction of marginal stability theory for one dimensional fronts.

cond-mat↗