Linear stability analysis on the onset of the Rayleigh–Taylor instability of a miscible slice in a porous medium

The onset of buoyancy-driven instability of a miscible high-density slice is analyzed theoretically using linear stability analysis. New stability equations are derived in the similarity domain and solved with and without quasi-steady-state approximation. In contrast with fingering between two semi-infinite regions, the fingering of a finite region is affected by the depth of the high-density slice. Through the initial growth rate analysis, it is shown that initially the system is unconditionally stable regardless of the depth of the high-density slice and there exists a most unstable initial condition. The effects of the depth of slice on the stability characteristics are systematically studied and compared with previous theoretical results. The present results show that there exists a critical time from which the disturbance starts to grow and the critical depth below which the growth rate is always negative, i.e., the system is unconditionally stable.