Linear Stability of Plane Poiseuille Flow over a Generalized Stokes Layer

Linear stability of plane Poiseuille flow subject to spanwise velocity forcing applied at the wall is studied. The forcing is stationary and sinusoidally distributed along the streamwise direction. The long-term aim of the study is to explore a possible relationship between the modification induced by the wall forcing to the stability characteristic of the unforced Poiseuille flow and the signifcant capabilities demonstrated by the same forcing in reducing turbulent friction drag. We present in this paper the statement of the mathematical problem, which is considerably more complex that the classic Orr-Sommerfeld-Squire approach, owing to the streamwise-varying boundary condition. We also report some preliminary results which, although not yet conclusive, describe the effects of the wall forcing on modal and non-modal characteristics of the flow stability.