MODE INTERACTIONS IN LARGE ASPECT RATIO CONVECTION

Mode interaction between odd and even modes in two-dimensional Boussin esq convection in a box is revisited. It is noted that in the large as pect ratio limit the structure of the amplitude equations depends on t he boundary conditions applied at the sidewalls, however distant. With no-slip sidewall boundary conditions the equations approach those for an unbounded layer with periodic boundary conditions; this is not the case for free-slip boundary conditions. Thus only in the former case can the large aspect ratio system be considered a small perturbation o f the unbounded system. The reasons for the different large aspect rat io limits are traced to the presence of ''hidden'' symmetries in the s tress-free case. Homotopic continuation is used to extend these result s to other types of boundary conditions.