Flow through a diverging channel: instability and bifurcation

The flow of a viscous fluid along a diverging channel is important practically. The mechanics of the flow also poses many theoretical problems. Some of these problems were considered before the foundation of the Japan Society of Fluid Mechanics, so it is perhaps surprising that their solutions are still so poorly understood. Nonetheless, a revival of interest in the last 20 years has led to progress in our understanding of the early stages of transition to turbulence in a two-dimensional channel. The present paper is a review of this progress in the theory of instabilities and bifurcations as the flux driven steadily along the channel is increased.