The calculation of eigenvalues for the stationary perturbation of couette-poiseuille flow

The problem considered is that of two-dimensional viscous flow in a straight channel. The decay of a stationary perturbation from the Couette-Poiseuille flow in the downstream is sought. A differential eigenvalue equation resembling the Orr-Sommerfeld equation is solved by using a spectral method and an initial-value method (the compound matrix method) for values of the Reynolds number R between 0 and 2000. The eigenvalues are presented for several of interesting cases with different measures of mass flux. These eigenvalues determine the rate of decay for the purturbation.