Axisymmetric cellular structures revisited
type: Item
instance of: scholarly article
title: Axisymmetric cellular structures revisited
zbMATH Open document ID: 0591.76062
DOI: 10.1007/BF00944631
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1985-01-01T00:00:00Z
review text: The authors consider weakly nonlinear axisymmetric cellular structures of the radius R near the onset of instability described by the following differential equation \([\epsilon -(\Delta +1)^ 2]A=A^ 3\), where A is a real function, \(\Delta\) is the Laplace operator, \(\epsilon\) is a parameter equal to the difference between the actual value of control parameter and the threshold value for an infinite pattern. Using a matching procedure it is shown that as soon as \(\epsilon\) is much bigger than \(R^{-2}\), the order of magnitude of A is \(\epsilon^{1/4}\) near the center and \(\epsilon^{1/2}\) outside. This prediction is confirmed by numerical analysis. The preceding results with an appropriate transposition are applied to Rayleigh-Bénard convection of Oberbeck- Boussinesq fluid between two rigid conducting plates.
Mathematics Subject Classification ID: 76E15
zbMATH DE Number: 3950004
zbMATH Keywords: weakly nonlinear axisymmetric cellular structures
zbMATH Keywords: onset of instability
zbMATH Keywords: control parameter
zbMATH Keywords: threshold value
zbMATH Keywords: matching procedure
zbMATH Keywords: Rayleigh-Bénard convection
zbMATH Keywords: Oberbeck-Boussinesq fluid
zbMATH Keywords: two rigid conducting plates
author: Yves Pomeau
author: Stéphane Zaleski
author: Paul Manneville
reviewed by: Andrzej Tylikowski
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00944631
OpenAlex ID: W1984903047
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description: scientific article; zbMATH DE number 3950004