**5. The pitchfork bifurcation flow in a symmetric 2D channel with contraction**

An important application is the study of the incompressible flow in a symmetric 2D channel with contraction.

Experimental and numerical research (see the works [26 – 32]) were performed in order to evaluate the flow through the 2D channel, especially after contraction occurs. The experiments done by Cherdron and Sobey (see [27], [28]) show the preferential formation of a recirculating zone on one of the channel walls, at a given Reynolds number. For values larger than the critical value Re*cr* , the flow through the channel loses its symmetry with respect to the channel summetry axis. This phenomenon is known as pitchfork bifurcation. Physically, in the fluid, a momentum transfer process occurs, causing the appearance of a pressure gradient across the channel. Such a pressure gradient may lead to an asymmetric flow. We refer to this phenomenon as the Coanda effect.
