Stability of Plane Poiseuille Flow to Periodic Disturbances of Finite Amplitude, II

Abstract

The stability of plane Poiseuille flow to periodic disturbances of finite amplitude was investigated by expanding each harmonic of the solution in terms of the Orr-Sommerfeld eigenfunctions with coefficients which are functions of time. The system of nonlinear ordinary differential equations for the coefficients was solved, and the number of harmonics N was extended from 3, of the previous investigation, to 5. The shift in the neutral curve in going from N = 3 to N = 5 is considerable, indicating insufficient convergence. The higher-order harmonics are effective because the zone of mode-coalescence rises with increasing N.