Non-modal Analysis of Buoyancy-Driven Instabilities in Porous Media of a Two-Layer Miscible Stratification in the Presence of Differential Diffusion

摘要

In a porous medium, a two-layer miscible stratification in the presence of differential diffusion is subject to buoyancy-briven instabilities for certain values of the parameters. For such systems, drawing reliable information from linear stability analysis is complex as the underlying base states are time evolving and the linearized operators are also non-normal. Here, we analyze the stability problem through the non-modal approach that takes these two features into account. For the delayed-double diffusive instability, it is shown that the non-modal analysis predictions are significantly different from those of the linear stability analysis based on the quasi-steady-state approximation. This is shown by considering the maximum amplification that the system can undergo and the wavenumber of the optimal perturbations.