Threshold Regimes in the Plane Channel Flow

Steady self-oscillations in the Poiseuille flow are calculated by using the approach concerning the resonance interaction between three waves: the plane wave with a certain fundamental frequency and three-dimensional half-frequency symmetrical couple. The problem is reduced to the eigenvalue problem for the system of nonlinear differential equations and is solved by the Newton method. The relation between the pulsation energy of the threshold regimes and the Reynolds number in the subcritical region has been obtained. The calculated results are in agreement with the experimental data for the transition in a plane channel.