The mechanism of drag reduction in turbulent pipe flow with spanwise wall oscillation

The results of a comparative analysis between turbulent pipe flow and drag reduced turbulent pipe flow by spanwise wall oscillation based upon a Karhunen-Lo\`{e}ve expansion are presented. The turbulent flow is generated by a direct numerical simulation at a Reynolds number $Re_\tau = 150$. The spanwise wall oscillation is imposed as a velocity boundary condition with an amplitude of $A^+ = 20$ and a period of $T^+ = 50$. The flow is driven by a constant pressure gradient, resulting in a 27\% mean velocity increase with wall oscillation. The peaks of the Reynolds stress and root-mean-squared velocities shift away from the wall and the Karhunen-Lo\`{e}ve dimension of the chaotic turbulence attractor is reduced from $2453$ to $102$. The coherent vorticity structures are pushed away from the wall into higher speed flow, causing an increase of their advection speed of 34\% as determined by a normal speed locus. The mechanism of drag reduction by spanwise wall oscillation is discussed.