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In linear and local stability analysis, the small amplitude disturbance behavior has been well understood for decades. In this context, convectively unstable flows act as noise amplifiers. In other words, a continuous excitation source at a fixed location triggers the spatial growth (or decay) of disturbances downstream of it. Hence, these flows have been traditionally analyzed using a spatial stability analysis, where disturbances are assumed temporally periodic and spatially unstable. Such a behavior has been consistently verified by direct numerical simulations. The present investigation shows that this agreement indeed occurs, but only close enough to the excitation source under certain parametric conditions. When the excitation source triggers disturbances that decay in space, far away from this source, spatially periodic and temporally unstable disturbances are allowed to grow and become dominant. Evidence for the scenario just described is provided using direct numerical simulations of the two-dimensional Prats problem. [ABSTRACT FROM AUTHOR]

Mixed convection in metallic foams modeled with Darcy's law under local thermal non-equilibrium conditions is investigated, where the solid phase thermal conductivity is assumed to be infinitely larger than its fluid phase counterpart. A linear and modal stability analysis was employed to evaluate the convective and absolute instability thresholds as well as their respective cell patterns. This analysis indicates that local thermal non-equilibrium always has a stabilizing effect and the spanwise uniform mode is always the most unstable. At the onset of convective instability, however, the number of equally unstable cell patterns increases with both the aspect ratio and the local thermal non-equilibrium strength. [ABSTRACT FROM AUTHOR]