A numerical study of two-dimensional instability-wave control based on the Orr–Sommerfeld equation

Abstract

A numerical method based on solution of the Orr–Sommerfeld equation is formulated to demonstrate the suppression of a two-dimensional, Tollmien–Schlichting-type, time-harmonic instability wave in a developing channel flow by a downstream secondary wave created through alternating suction and blowing at the surface. An analytical expression is derived providing the amplitude and a second parameter (the width or the phase) of the downstream surface-velocity distribution required to create a wave that will suppress the downstream continuation of the original disturbance.