Abstract
Nonlinear behaviour of the two-dimensional disturbances in a plane Poiseuille flow is investigated by three different methods. Firstly, nonlinear neutral surfaces are calculated by the Newton-Raphson method to resolve the question of Itoh (1986) why his result does not coincide with that of Herbert (1976). Secondly, we perform numerical simulation to show that the nonlinear neutral surfaces obtained by the Newton-Raphson method are attainable asymptotically by the dynamical solution starting from an arbitrary initial condition. Lastly, we investigate the nonlinear development of disturbances by weakly nonlinear stability theory and compare the results with those obtained by the numerical simulation.
