Transport in Porous Media 37: 213–245, 1999. © 1999 Kluwer Academic Publishers. Printed in the Netherlands. 213 Local and Global Transitions to Chaos and Hysteresis in a Porous Layer Heated from Below PETER VADASZ Department of Mechanical Engineering, University of Durban-Westville, Private Bag X54001, Durban 4000, South Africa (Received: 12 May 1998; in final form: 29 October 1998) Abstract. The routes to chaos in a fluid saturated porous layer heated from below are investig- ated by using the weak nonlinear theory as well as Adomian’s decomposition method to solve a system of ordinary differential equations which result from a truncated Galerkin representation of the governing equations. This representation is equivalent to the familiar Lorenz equations with different coefficients which correspond to the porous media convection. While the weak nonlinear method of solution provides significant insight to the problem, to its solution and corresponding bifurcations and other transitions, it is limited because of its local domain of validity, which in the present case is in the neighbourhood of any one of the two steady state convective solutions. On the other hand, the Adomian’s decomposition method provides an analytical solution to the problem in terms of infinite power series. The practical need to evaluate numerical values from the infinite power series, the consequent series truncation, and the practical procedure to accomplish this task transform the otherwise analytical results into a computational solution achieved up to a finite accuracy. The transition from the steady solution to chaos is analysed by using both methods and their results are compared, showing a very good agreement in the neighbourhood of the convective steady solutions. The analysis explains previously obtained computational results for low Prandtl number convection in porous media suggesting a transition from steady convection to chaos via a Hopf bifurcation, represented by a solitary limit cycle at a sub-critical value of Rayleigh number. A simple explanation of the well known experimental phenomenon of Hysteresis in the transition from steady convection to chaos and backwards from chaos to steady state is provided in terms of the present analysis results. Key words: chaos, free convection, weak turbulence, Lorenz equations. Nomenclature Latin symbols Da Darcy number, defined by k ∗ /H 2 ∗ . ˆ e x unit vector in the x direction. ˆ e y unit vector in the y direction. ˆ e z unit vector in the z direction. ˆ e g unit vector in the direction of gravity. ˆ e n unit vector normal to the boundary, positive outwards. H ∗ the height of the layer. H the front aspect ratio of the porous layer, equals H ∗ /L ∗ . k ∗ permeability of the porous domain.