The receptivity problem of boundary-layer flows and bifurcations of periodic regimes

The method of the invariant finite-dimensional projections of the Navier-Stokes equations is applied to a plane-parallel flow of a viscous incompressible fluid over a flat semi-infinite plate. Thus the initial-boundary problem for periodic disturbances of main flow is reduced to finite-dimensional recurrent system of linear boundary problems for the ordinary differential equations. The proposed universal algorithm allow to calculate amplitude surfaces of unstable and stable regimes and points of tangential bifurcation of periodic modes for arbitrary frequencies and Reynolds numbers. Comparison of numerical results with the receptivity problem and experiments in laminar-turbulent transition is spent.