Dynamics of propagating turbulent pipe flow structures. Part I: Effect of drag reduction by spanwise wall oscillation

The results of a comparative analysis based upon a Karhunen-Lo\`{e}ve expansion of turbulent pipe flow and drag reduced turbulent pipe flow by spanwise wall oscillation 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 wall oscillation results in a 27% mean velocity increase when the flow is driven by a constant pressure gradient. 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 turbulent 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. This increase in advection speed gives the propagating waves less time to interact with the roll modes. This leads to less energy transfer and a shorter lifespan of the propagating structures, and thus less Reynolds stress production which results in drag reduction.