Nonlinear Study of Hydrodynamic Rayleigh-Taylor Instability in a Composite Fluid-Porous Layer

The nonlinear hydrodynamic Rayleigh-Taylor instability (RTI) bounded above by porous layer using Saffman [1] slip condition at the interface and below by a rigid surface using no-slip condition has been studied. The nonlinear problem is studied numerically in the present paper using Adams-Bashforth predictor and Adams-Moulton corrector numerical techniques. In the conclusion, the nonlinear problem discussed here is quite different from that of Babchin et al. [2] considering plane Couette flow. The present problem is greatly influenced by slip velocity at the interface between porous layer and thin film. Also, the effect of magnetic field to stabilize the system. It is not amenable to analytical treatment as that of Babchin et al.[2]. Therefore, numerical solutions have to be found. Fourth order accurate central differences are used for spatial discretization using predictor and corrector numerical technique.