Weak turbulence and chaos for low Prandtl number gravity driven convectionin porous media

Low Prandtl number convection in porous media is relevant to modern applica tions of transport phenomena in porous media such as the process of solidif ication of binary alloys. The transition from steady convection to chaos is analysed by using Adomian's decomposition method to obtain an analytical s olution in terms of infinite power series. The practical need to evaluate t he solution and obtain numerical values from the infinite power series, the consequent series truncation, and the practical procedure to accomplish th is task, transform the analytical results into a computational solution eva luated up to a finite accuracy. The solution shows a transition from steady convection to chaos via a Hopf bifurcation producing a 'solitary limit cyc le' which may be associated with an homoclinic explosion. This occurs at a slightly subcritical value of Rayleigh number, the critical value being ass ociated with the loss of linear stability of the steady convection solution . Periodic windows within the broad band of parameter regime where the chao tic solution persists are identified and analysed. It is evident that the f urther transition from chaos to a high Rayleigh number periodic convection occurs via a period halving sequence of bifurcations.