Bifurcations of a plane parallel flow with Kolmogorov forcing

We study the primary bifurcations of a plane parallel flow in a channel with Kolmogorov forcing. We find a new type of bifurcation with both the oscillation frequency and the amplitude of the growing mode being zero at the threshold. We call this a stationary drift bifurcation. The laminar steady flow can display different types of bifurcation depending on the forcing wave number of the base flow. This is in contrast to the case of doubly periodic boundary conditions for which the primary bifurcation is stationary.