Hopf Bifurcation in Viscous Incompressible Flow Down an Inclined Plane: a Numerical Approach

In this article we investigate numerically a Hopf bifurcation phenomenon for a viscous incompressible flow down an inclined plane. This problem has been discussed by Nishida et al. who proved the existence of periodic solutions bifurcating from the steady flow. Using a computational methodology based on finite elements for the space discretization and on operator splitting for the time discretization, we have been able to reproduce the results predicted by Nishida et al.