Solutions of the Ginzburg‐Landau Equation of Interest in Shear Flow Transition

Abstract

The Ginzburg‐Landau equation may be used to describe the weakly nonlinear 2‐dimensional evolution of a disturbance in plane Poiseuille flow at Reynolds number near critical. We consider a class of quasisteady solutions of this equation whose spatial variation may be periodic, quasiperiodic, or solitarywave‐ like. Of particular interest are solutions describing a transition from the laminar solution to finite amplitude states. The existence of these solutions suggests the existence of a similar class of solutions in the Navier‐Stokes equations, describing pulses and fronts of instability in the flow.