Flow and Double-Di usive Instability in Porous Media

Abstract

The ow and double-di usive instability in porous media has been studied in this work. The linear perturbation theory has been utilised for both thermal convection and double-di usive convection. We found that for the thermal convection, below the critical Rayleigh number, the system is stable and above that number the system is unstable. For the double-di usive convection, the stability transition has two di erent behaviour: when the concentration gradient is negative, the perturbations are in exponential form. When it is positive, we observe the oscillatory mode. The weakly non-linear stability analysis has been studied using the Galerkin approximation approach and we found that for di erent values of Rayleigh number, the solutions bifurcate. Using numerical simulations, we found that when the base state is unstable, the perturbations do not grow forever but saturate at a nite amplitude; however the nite-amplitude solution is not a global attractor.