European Journal of Applied Mathematics

Table of Contents - 1994 - Volume 5, Issue 03  

Research Article

Finite amplitude convection between stress-free boundaries; Ginzburg–Landau equations and modulation theory

Andrew J. Bernoffa1 p1

a1 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK

Abstract

The stability theory for rolls in stress-free convection at finite Prandtl number is affected by coupling with low wavenumber two-dimensional mean-flow modes. In this work, a set of modified Ginzburg–Landau equations describing the onset of convection is derived which accounts for these additional modes. These equations can be used to extend the modulation equations of Zippelius & Siggia describing the breakup of rolls, bringing their stability theory into agreement with the results of Busse & Bolton.

(Received March 22 1993)

Correspondence:

p1 Present address: Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208-3125, USA.