Direct Numerical Simulations of Non-linear Time Periodic Flows in a Planar Channel

Details of understanding non-linear time-periodic wall flows are of interest to engineering applications in biomedical and environmental flows. Non-linearity in wall-bounded time-periodic flows, due to higher frequency contribution to the velocity and/or acceleration in the outer layer, significantly alters the wall turbulence. The most striking example is the formation of a net current in the opposite direction of the wave propagation. Here, we present the results of direct numerical simulations of a flow over a smooth wall, driven by a Stokes Second-order Wave (SOSW). Channel flow driven by SOSW has a skewed velocity but symmetric acceleration in the outer region. This allows us investigate the role of velocity skewness to the wall turbulence. Our results suggest that the velocity skewness in the outer region leads to a skewness in the friction velocity and the viscous length scale. The difference of viscous length scale, between the crest and the trough of the wall shear stress, creates a wall-normal offset in Reynolds shear stress during the positive and negative flow. This gives a net Reynolds shear stress,  if integrated over a cycle,  and creates a net flow. How net flow characteristics changes with respect to Reynolds number is further discussed in this presentation.