Scalings of Rayleigh-Taylor Instability at Large Viscosity Contrasts in Porous Media

The scalings of the Rayleigh-Taylor instability are studied numerically for porous media flows when the denser fluid lying on top of the less dense one is also much more viscous. We show that, above a critical value of the viscosity ratio $M$, a symmetry breaking of the buoyancy-driven fingers is observed as they extend much further downward than upward. The asymmetry ratio scales as ${M}^{1/2}$ while the asymptotic flux across the initial contact line, quantifying the mixing between the two fluids, scales as ${M}^{\ensuremath{-}1/2}$. A new fingering mechanism induced by large viscosity contrasts is identified and shows good agreement with experimentally observed dynamics.