The flow of a viscous fluid along a diverging channel is important practica
lly. The mechanics of the flow also poses many theoretical problems. Some o
f these problems were considered before the foundation of the Japan Society
of Fluid Mechanics, so it is perhaps surprising that their solutions are s
till so poorly understood. Nonetheless, a revival of interest in the last 2
0 years has led to progress in our understanding of the early stages of tra
nsition 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 (C) 1999 The Japan
Society of Fluid Mechanics and Elsevier Science B.V, All rights reserved.