Gravitational instability of miscible fluids in a Hele-Shaw cell

We revisit the Rayleigh–Taylor instability when the two fluids are miscible and in the geometry of a Hele-Shaw cell. We provide analytical dispersion relations for the particular cases of either a sharp front between the two fluids or of a uniform density gradient stratification and for various fluid flow models, including an unbounded geometry, a two-dimensional gap-averaged Navier–Stokes–Darcy equation, and an effective porous medium. The results are compared to three-dimensional lattice BGK simulations, based on which the relevance of the various models in different wavelength regimes is discussed.