Convection patterns in large aspect ratio systems

M. C. Cross, Alan C Newell

Research output: Contribution to journalArticle

189 Citations (Scopus)

Abstract

A theory, which should have widespread application, is developed to treat the statics and slow dynamics of patterns of convective rolls encountered in large aspect ratio Rayleigh-Bénard boxes. For case of presentation the theory is developed using model equations. Wavenumber selection, the shape of patterns, stability and the time dependence resulting from long wavelength instabilities are discussed. The effects of adding the local mean drift important in low Prandtl number situations are investigated. Our theory includes the notion of the Busse stability balloon, reduces near critical values of the stress parameter to the Newell-Whitehead-Segel equations, and contains the Pomeau-Manneville phase equation. It also gives a detailed description of the way in which the field amplitude, which is slaved to the phase gradient away from threshold, becomes an independent order parameter near the critical point.

Original languageEnglish (US)
Pages (from-to)299-328
Number of pages30
JournalPhysica D: Nonlinear Phenomena
Volume10
Issue number3
DOIs
StatePublished - 1984

Fingerprint

Aspect Ratio
Convection
aspect ratio
Aspect ratio
convection
Balloon
Balloons
Prandtl number
Time Dependence
balloons
Rayleigh
Order Parameter
time dependence
boxes
Critical value
Critical point
critical point
Wavelength
Gradient
gradients

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

Convection patterns in large aspect ratio systems. / Cross, M. C.; Newell, Alan C.

In: Physica D: Nonlinear Phenomena, Vol. 10, No. 3, 1984, p. 299-328.

Research output: Contribution to journalArticle

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