Diffusive stabilization of density-driven instability in contaminated aquifers: Analytical and numerical study

Density-driven convective instabilities in porous media control the migration of contaminant plumes in aquifers. We present a comprehensive theoretical and numerical study of miscible Rayleigh–Taylor instability in unbounded porous media, where diffusion acts as a strong stabilizing mechanism that delays instability onset. Using a modified quasi-steady state approximation, we derive analytical expressions for the critical time and the wavelength of maximum growth. The analytical solution is obtained using a piecewise-linear approximation of the diffusive concentration profile. Despite this simplification, the theory accurately predicts the critical time for instability onset. Direct numerical simulations validate the theory in critical time prediction and agreement in growth rates during the linear regime. The results provide quantitative criteria for assessing when density-driven instabilities become significant in contaminated aquifers, informing monitoring network design, remediation strategy selection, and long-term risk assessment for groundwater protection.