a1 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK
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)
p1 Present address: Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208-3125, USA.