Linear and Nonlinear Analyses of the Onset of Buoyancy-Induced Instability in an Unbounded Porous Medium Saturated by Miscible Fluids

This study analyzes the stability of an initially sharp interface between two miscible fluids in a porous medium. Linear stability equations are first derived using the similarity variable of the basic state, and then transformed into a system of ordinary differential equations using a spectral expansion with and without quasi-steady-state approximation (QSSA). These transformed equations are solved using the eigenanalysis and initial value problem approach. The initial growth rate analysis shows that initially the system is unconditionally stable. The stability characteristics obtained under the present QSSA are quantitatively same as those obtained without the QSSA. To support these theoretical results, numerical simulations are conducted using the Fourier-spectral method. The results of theoretical linear stability analyses and the numerical simulations validate to each other.