Vortex-Wave interaction in plane Poiseuille flow

Our main interest is in the process of transition to turbulence at high Reynolds numbers in the flow in a plane channel. We will consider the basic flow to be driven by a uniform streamwise pressure gradient (plane Poiseuille flow). We will formulate a high Reynolds number asymptotic structure in the form of a nonlinear vortex-Tollmien-Schlichting-wave interaction (VWI)- or so-called self sustaining process. We look for starting solutions for the VWI by performing a weakly nonlinear analysis close to the lower branch neutral point and seek equilibrium solutions of the resulting nonlinear amplitude equation. We provide numerical solutions of the interaction equations which are localised in the spanwise direction at large enough amplitudes.