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Competition between Spiral-Defect Chaos and Rolls in Rayleigh-Benard Convection
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Accepted as Rapid Comm in PRE
Competition between Spiral-Defect Chaos and Rolls in
Rayleigh-Be?nard Convection
Kapil M. S. Bajaj, David S. Cannell, and Guenter Ahlers
Department of Physics and Center for Nonlinear Science, University of California, Santa
Barbara, California 93106, USA
(February 9, 2008)
Abstract
We present experimental results for pattern formation in Rayleigh-Be?nard
convection of a fluid with a Prandtl number σ ? 4. We find that the spiral-
defect-chaos (SDC) attractor which exists for σ ? 1 has become unstable.
Gradually increasing the temperature difference ?T from below to well above
its critical value ?Tc no longer leads to SDC. A sudden jump of ?T from below
to above ?Tc causes convection to grow from thermal fluctuations and does
yield SDC. However, the SDC is a transient; it coarsens and forms a single
cell-filling spiral which then drifts toward the cell wall and disappears.
PACS numbers: 47.54.+r,47.20.Lz,47.27.Te
Typeset using REVTEX
1
Rayleigh-Be?nard convection (RBC) occurs in a shallow horizontal layer of a fluid heated
from below when the temperature difference ?T across the layer exceeds a critical value ?Tc.
The velocity fields which form above ?Tc have long been used as an experimental testing
ground for theories of pattern formation in nonlinear systems. [1] The phenomena which
occur depend upon the Prandtl number σ = ν/κ, the dimensionless ratio of the kinematic
viscosity ν to the thermal diffusivity κ. A fascinating recent discovery in RBC is that of
spiral-defect chaos (SDC) for σ ? 1. [2] It consists of patches of rotating convection-roll
spirals and of other defects, and occurs for ? ≡ ?T/?Tc ? 1 ?s 0. The spirals are
coherent structures with a typical diameter of a few roll wavelengths. They can be right-
or left-handed, single- or multi-armed, and appear and disappear irregularly in time and
space. SDC has since been found in numerical solutions of mo
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