An instability analysis in a horizontal porous layer is made for a fluid with an inverse density gradient. The governing equations resulted when instability analysis is applied to this problem, are non-linear and therefore mathematically complex. In published literature, the problem is solved with some simplifications such as ignoring certain terms in the governing equations, or finding algebraic approximations that are valid in some specific range of physical parameters.
In this study, the problem is solved in its general form for two rigid, and one rigid and one free boundary conditions using variational methods. The resulting critical Rayleigh numbers and critical wave numbers vs. l2/K curves are compared to previous works.