THE 3-DIMENSIONAL STABILITY OF FINITE-AMPLITUDE CONVECTION IN A LAYERED POROUS-MEDIUM HEATED FROM BELOW

Landau-Ginzburg equations are derived and used to study the three-dimensional stability of convection in a layered porous medium of infinite horizontal extent. Criteria for the stability of convection with banded or square planform are determined and results are presented for two-layer and symmetric three-layer systems. In general the neutral curve is uni-modal and parameter space is divided into regions where either rolls or square cells are stable. For certain ranges of parameters, however, the neutral curve is bimodal and there exists a locus of parameters where two modes with different wavenumbers have simultaneous onset. © 1990, Cambridge University Press. All rights reserved.