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

Dynamics of a 1-D model for the emergence of the plasma edge shear flow layer with momentum conserving Reynolds stress