The Rayleigh-Taylor instability of an incompressible fluid through porous medium (Q1108152)

The Rayleigh-Taylor instability of an incompressible, viscous, rotating conducting fluid through porous medium with a vertical magnetic field is examined. It has been shown that the solution is characterized by a variational principle. Based on the existence of variational principle, an approximate solution has been derived for the case of a fluid of finite depth and having exponentially varying density. It has been found that the statistically unstable configuration is rendered unstable for entire wave-length band due to joint effects of permeability of the medium, viscosity and finite resistivity. The behaviour of growth rates with respect to medium permeability are examined analytically.