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.
