  We study miscible Rayleigh-Taylor (RT) fingering instability in
two-dimensional homogeneous porous media, in which the fluid density varies
non-monotonically as a function of the solute concentration such that the
maximum density lies in the interior of the domain, thus creating a stable and
an unstable density gradients that evolve in time. With the help of linear
stability analysis (LSA) as well as nonlinear simulations the effects of
density gradients on the stability of RT fingers are investigated. As diffusion
relaxes the concentration gradient, a non-monotonic density profile emerges in
time. Our simple mathematical treatment addresses the importance of density
gradients on the stability of miscible Rayleigh-Taylor fingering. In this
process we identify that RT fingering instabilities are better understood
combining Rayleigh number (Ra) with the density gradients--hence defining a new
dimensionless group, gradient Rayleigh number (Ra$_g$). We show that
controlling the stable and unstable density gradients, miscible Rayleigh-Taylor
fingers are controllable.
