Time-evolving to space-evolving Rayleigh–Bénard instability of a horizontal porous medium flow

The Rayleigh–Bénard instability of the stationary throughflow in a horizontal porous layer, also known as Prats' problem, is analyzed here in a fresh new perspective. In fact, the classical analysis of linear instability, carried out by employing time-evolving and space-periodic Fourier modes, is reconsidered here by focusing on the effects of time-periodic and space-evolving modes. The basic stationary flow is assumed to be perturbed by a localized source of perturbation that is steady-periodic in time. Then, the spatial development of such perturbations is monitored in order to detect their possible amplification or decay in their direction of propagation. Accordingly, the spatial stability/instability threshold is determined. The study is carried out by employing a Fourier transform formalism, where the transformed variable is time.