Effects of Longitudinal Wall-Oscillation on Transition of a Channel Flow

Abstract

Effects of longitudinal wall-oscillation on transition of a channel flow are investigated by Direct Numerical Simulation (DNS) and linear stability analysis. Reynolds number defined by the mean flow and the distance of walls is fixed at 10000 in convenience. In the remaining parameters of wall frequency and amplitude, parametric study shows that the parameter space can roughly be divided on to three parts. In the first part, the transition occurs rapidly. It may relates the transient growth in the channel flow. In the other parts, the transition is accelerated or decelerated. From the visualization study based on the vorticity, we observed that the growth of streak like structures near the walls are suppressed in the accelerated case. For the linear stability analysis, the basic flow is given by a superimposition of the channel flow and the Stokes layer because both flow can be written as a solution of the linearized Navier-Stokes equation. Using this flow, the linear stability analysis shows that the effect of the parameters on the transition roughly corresponds to the results of DNS. Moreover, it seems that the rapid transition has correlation with the stability of the Stokes layer flow.