NONLINEAR-INTERACTION OF CONVECTIVE INSTABILITIES AND TEMPORAL CHAOS OF A FLUID MIXTURE IN A POROUS-MEDIUM

A possible route to temporal chaos is proposed as a result of a nonlin ear interaction between convective instabilities in a fluid mixture co ntained within a porous medium when temporal fluctuations in the tempe rature are present. In the absence of fluctuations, and in a certain r ange of the parameters, it is well known according to linear stability analysis that there exists a codimension two bifurcation. In a previo us work [Ouarzazi & Bois, 1993] we showed that, far from the polycriti cal point, fluctuations lead to a small shift in bifurcating curves. H ere it is found that near the codimension two bifurcation, the nonline ar interaction between convective instabilities together with the effe ct of fluctuations can drastically change the global dynamic behaviour even for small amplitude fluctuations. Thus, a temporal chaotic regim e may occur in the system. A reduction to amplitude equations allows u s, by means of Melnikov's techniques, to derive analytically bifurcati on curve for nonlinear resonances and the threshold for the onset of S male horseshoe chaos. Numerical simulations are given and are in good agreement with the theoretical predictions.