Axisymmetric cellular structures revisited
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.
weakly nonlinear axisymmetric cellular structures
scientific article; zbMATH DE number 3950004
scientific article