Nonlinear dynamics of an interface in an inclined channel

Here we consider the gravity-driven dynamics of two superposed, incompressible, immiscible, viscous fluids flowing in a parallel-wall channel. The fluids are governed by the Navier-Stokes equations with surface tension along the interface. We use the front tracking numerical method to determine the solutions. Both stable and unstable solutions are obtained. The unstable solutions are characterized by a finger of lower fluid rising into the upper fluid. Our results are consistent with the predictions of linear stability theory. In addition, we attempt to characterize the growth of the unstable solutions as a function of the Reynolds and the Bond number. (C) 2002 American Institute of Physics.