On origin of unstable modes in viscous channel flow subject to periodically distributed surface suction

The linear stability of a flow in a channel subject to periodically distributed suction applied at the walls is investigated. The focus is on the relation between unstable modes observed in such a flow and the stability properties of the flow without suction (the Poiseuille flow). It is demonstrated that linearly unstable modes appearing in the presence of suction can be interpreted as modified Orr-Sommerfeld's or Squire's eigenmodes of the Poiseuille flow. Originally, these modes have the streamwise wave number equal to zero, i.e. they are invariant in the streamwise direction. When the surface suction is applied, the modes are additionally modulated along the channel and they become dependent on the streamwise variable. In the range of the parameters studied, a pair of such modes, one Orr-Sommerfeld's and one Squire's, can be simultaneously unstable. Certain properties of these modes are discussed in some details. Specifically, the influence of non-symmetric suction on stability characteristics is analysed.