  A one-dimensional version of the second-order transition model based on the
sheared flow amplification by Reynolds stress and turbulence supression by
shearing is presented. The model discussed in this paper includes a form of the
Reynolds stress which explicitly conserves momentum. A linear stability
analysis of the critical point is performed. Then, it is shown that the
dynamics of weakly unstable states is determined by a reduced equation for the
shear flow. In the case in which the flow damping term is diffusive, the
stationary solutions are those of the real Ginzburg-Landau equation.
