Floquet Stability Analysis of a Channel Flow with Longitudinal Wall Oscillation

Stability of the channel flow with longitudinal wall‐oscillation is investigated by the Floquet theory. The stability equation, time‐dependent Orr‐Sommerfeld equation, is rewritten as a simple ordinary differential equation by the use of the collocation method. Using this ordinary equation, the Floquet exponents are defined. The velocity profiles for the Floquet analysis are given as superimposition of the two dimensional plane Poiseuille flow with the Stokes layer. Reynolds number is fixed at 10 000 which corresponds to supercritical condition. The parametric study shows that there is a stability spot on the parameter space in spite of the supercritical condition.