NONLINEAR STABILITY ANALYSIS OF PLANE POISEUILLE FLOW BY NORMAL FORMS

In the subcritical interval of the Reynolds number 4320 less than or e qual to R less than or equal to R(c) equivalent to 5772, the Navier-St okes equations of the two-dimensional plane Poiseuille Row are approxi mated by a 22-dimensional Galerkin representation formed from eigenfun ctions of the Orr-Sommerfeld equation. The resulting dynamical system is brought into a generalized normal form which is characterized by a disposable parameter controlling the magnitude of denominators of the normal form transformation. As rigorously proved, the generalized norm al form decouples into a low-dimensional dominant and a slaved subsyst em. From the dominant system the critical amplitude is calculated as a function of the Reynolds number. As compared with the Landau method, which works down to R = 5300, the phase velocity of the critical mode agrees within 1%; critical amplitude is reproduced similarly well exce pt close to the critical point where the maximal error is about 16%. W e also examine boundary conditions which partly differ from the usual ones.