Subcritical instability of Stokes layer induced by wall surface roughness

The subcritical instability problem of a finite Stokes layer over two-dimensional wall surface roughness was investigated by numerical simulations. Results indicated that infinitesimal height of roughness led to a quite large deviation of the response curves from the linear cases. With the increasing height of wall roughness, the evolution of the disturbance at one order spectrum displayed the sub-harmonic component, and then the evolution entered into the irregular state, indicating the subcritical instability. According to the correlation between the height of roughness and the disturbance at one order spectrum evolution, the critical height of roughness was defined, and the relation curve was given as a result. Results shows that the critical height of roughness becomes smaller as the Reynolds number increases. At the Reynolds number around 300, the height of roughness of just the level of micrometer would be able to trigger the subcritical instability and transition in Stokes layer. That is why transition often occurs in experimental observations at Reynolds number around 300.