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 nonlinear interaction between convective instabilities in a fluid mixture contained within a porous medium when temporal fluctuations in the temperature are present. In the absence of fluctuations, and in a certain range of the parameters, it is well known according to linear stability analysis that there exists a codimension two bifurcation. In a previous work [Ouarzazi & Bois, 1993] we showed that, far from the polycritical point, fluctuations lead to a small shift in bifurcating curves. Here it is found that near the codimension two bifurcation, the nonlinear interaction between convective instabilities together with the effect of fluctuations can drastically change the global dynamic behaviour even for small amplitude fluctuations. Thus, a temporal chaotic regime may occur in the system. A reduction to amplitude equations allows us, by means of Melnikov's techniques, to derive analytically bifurcation curve for nonlinear resonances and the threshold for the onset of Smale horseshoe chaos. Numerical simulations are given and are in good agreement with the theoretical predictions.