Nonlinear Rayleigh-Taylor instability for hydromagnetic Darcian flow: effect of free surface currents

摘要

Capillary-gravity waves of permanent form at the interface between two unbounded magnetic fluids in porous media are investiagted The system is influenced by the horizntal direction of th emagnetic field ot the separation face of two semi-infinite homogeneous and incompressible fluids so that the fields allow free-surfae currents at the interface The solutions of the linearized equation of motion under nonlinear bounday conditions lead to derivation of a nonlinear equation governing the interfacial disphacement This equation is saccomplished by using the cubic njonlinearity Taylor theory is used to expand the governing nonlinear equation in hte light of the multiple scales in both space and time The perturbation analysis leads to imposition of two levels of solvability conditions which are usee to construct the well-known nnlinear Ginzbur-Landau euation The stability criteria are discussed theoretically and numbericallyi and stability diagrams are obtained Regions of stbility and instability are identified for the surface current density It is found that the stabilizing role for the magnetic field is tetarded when the flow is in porous media Moreover the increase in the values of resistance parameters plays a dual role in stability behavior and in the increase in surface current density.