Asymptotic structure of wave disturbances in the stability theory of a plane Couette–Poiseuille flow

The stability of a plane Couette–Poiseuille flow is analyzed in the case of Reynolds numbers tending to infinity. Dispersion relations connecting the parameters of linear eigenoscillations are derived by asymptotic methods. The relations possess qualitatively new properties lacking in the case of the Poiseuille flow. The perturbation pattern depends strongly on the relation between the Reynolds number and the wall velocities. Four characteristic regimes can be distinguished for which there are neutral (or nearly neutral) modes in the spectrum of eigenoscillations.