Abstract
We considered an incompressible fluid-saturated porous layer bounded by
two infinite parallel plates. Boussinesq approximation and Darcy’s law
are applied. The permeability is assumed to be a linear function of the
depth $z$. The linear stability is investigated. The long wavelength
expansion method is applied to conduct the weakly nonlinear stability
analysis. The evolution equation is derived and analyzed. A uniformly
valid periodic solution of the evolution equation is obtained by the
application of Poincar\’e-Lindstedt method. Some
numerical simulations is presented.