STABILIZING EFFECT OF LONGITUDINAL WALL OSCILLATION ON 2D CHANNEL FLOW

摘要

The present study investigates a stabilizing effect of longitudinal wall-oscillation on two dimensional channel flow by the Floquet theory. To apply this theory to the present periodic flow, a time-dependent Orr-Sommerfeld equation is discritized using the collocation points. The velocity profile needed in this analysis is calculated by superposition of the plane Poiseuille flow and the Stokes layer because of the linearity of the governing equation. In this study, the Reynolds number, which is defined by maximum mean-flow velocity and a half width between the two walls, is fixed to 10,000 that corresponds to the turbulent state of usual channel flow. When the remaining two parameters, frequency and amplitude of the wall-oscillation, are changed parametrically, it is found that on the parameter space the stable region exists even under the supercritical condition. The direct numerical simulation (DNS) also carried out to validate this feature. DNS demonstrates that the transitional period to the fully turbulent state is longer or shorter compared with non-oscillating case depending on the parameters mentioned above. The comparison of the results obtained the Floquet analysis with DNS shows that the stable region in the Floquet analysis roughly coincides with the region of slow transition.