Transport in Porous Media, Vol.85, No.2, 415-435, 2010
The Vadasz-Olek Model Regarded as a System of Coupled Oscillators
The Vadasz-Olek model of chaotic convection in a porous layer is revisited in this article The first-order differential equations of this Lorenz-type model are transformed in the governing equations of a damped nonlinear oscillator, modulated by a linear degenerated overdamped oscillator (relaxator) which in turn is coupled to former one by a nonlinear cross force The benefit of this mechanical analogy is an intuitive picture of the regular and chaotic dynamics described by the Vadasz-Olek model Thus, there turns out that the "eyes" of the chaotic attractor correspond to the minima of the potential energy of the modulated nonlinear oscillator having a double-well shape Several new aspects of the subcritical and supercritical dynamic regimes are discussed in some detail
Keywords:Porous layer;Chaotic convection;Strange attractors;Nonlinear oscillations;Damping;Modulation