ABSOLUTE INSTABILITY OF A NEWTONIAN FLUID SATURATING A POROUS LAYER HEATED FROM BELOW

We study a horizontal porous layer heated from below and saturated with a Newtonian fluid flowing horizontally between two impermeable plates. In such a system, there are two critical instability thresholds: the convective and the absolute instabilities. In this paper, the zone beyond the threshold of absolute instability has been studied both analytically and numerically by implementing a spatiotemporal analysis. First, we show how the linear stability analysis is conducted, and by applying the two conditions of absolute instability to the dispersion equation, we find the instability occurrence thresholds. The linear stability analysis has revealed that Rayleigh number at the absolute instability threshold is situated beyond 4π<sup>2</sup> (the convective critical threshold for Rayleigh number) in a porous medium. We use a two-dimensional finite difference method to conduct the numerical simulations and compare the results with both analytical results and previous studies. We study the influence of the governing nondimensional parameters of the system (Péclet and Rayleigh numbers) on oscillation frequency and wave number both analytically and numerically. We also illustrate how the presence of a filtration flow influences results with a Newtonian fluid in the supercritical state beyond the absolute instability threshold. In the end, we discuss the numerical establishment length and try to validate the Landau law of scale with our results.