Role of density gradients on miscible Rayleigh-Taylor fingers in porous media

We investigate the effect of density gradients on miscible Rayleigh-Taylor fingers in homogeneous porous media using two families of concentration-dependent density profiles: (a) monotonic and (b) nonmonotonic. The first family consists of linear, quadratic, and cubic functions of the solute concentration, while the latter is described as a quadratic function of the solute concentration such that the density maximum (minimum) appears in time as diffusion relaxes the concentration gradient. With the help of these simple models, we are able to address one of the most puzzling questions about the fingering instabilities with nonmonotonic density profiles. Using linear stability analysis and nonlinear simulations, we show that density gradients play a pivotal role in controlling instability.