Convective and absolute instability of horizontal flow in porous media

Abstract

The onset of instability in flow systems has a dual nature depending on the dynamics of the growing normal modes. When the time evolution of a wave packet perturbation is tested, the growth of individual Fourier normal modes can be concealed to an observer in the laboratory reference frame. The reason is that the growing mode can be convected away by the basic flow, so that no effective growth is detected for the wave packet. The convective instability just focusses on the dynamics of each Fourier mode of perturbation, disregarding the actual amplitude growth of a wave packet, measured at a given position. When not only the Fourier modes, but all localised wave packets grow in time at a given position, then the instability becomes absolute. The two types of instability are generally distinct. This paper illustrates the transition from convective to absolute instability starting from a simple one-dimensional case. Then, this concept is employed for the stability analysis of a porous medium flow with heating from below. While the one-dimensional flow system is studied analytically, the porous medium flow stability is investigated numerically.