On a Linear Stability Problem Related to Underground CO₂ Storage

The analysis of gravitational instability of a diffusive boundary layer in porous media has been addressed in several papers over the years. In this paper we consider the linear stability problem for an infinite depth aquifer with anisotropic absolute permeability. We derive an explicit expression for the time evolution equations of the generalized Fourier coefficients corresponding to the linear stability problem. This allows us to study linear stability properties through the spectra of infinite symmetric matrices, showing excellent agreement with previously published results derived using the so-called quasi-static method.