Sudden and Smooth Transitions to Weak Turbulence in Porous Media Convection

The fundamental understanding of the transition from laminar to turbulent convection in porous media is far from being conclusive. In isothermal flow in porous media no experiments identifying the three dimensional nature of a transition from the Darcy regime, via an inertia dominated regime, towards turbulence are available. In particular this detailed description of turbulence is missing in the problem of porous media convection where an additional non-linear interaction appears as a result of the coupling between the equations governing the fluid flow and the energy equation. The latter can typically cause a transition to a non-steady and non-periodic regime (referred to as weak turbulent) at much lower values of the parameter controlling the flow, when compared to the corresponding isothermal system. The present paper identifies the conditions for sudden and smooth transitions. In addition it attempts to address the question related to the reason for the subcritical transition to weak turbulence and the existence of a range of values of the porous media Rayleigh number over which the transition occurs, i.e. the Lorenz attractor.