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It is well known that drag created by turbulent flow over a surface can be reduced by oscillating the surface in the direction transverse to the mean flow. Efforts to understand the mechanism by which this occurs often apply the solution for laminar flow in the infinite half-space over a planar, oscillating wall (Stokes’ second problem) through the viscous and buffer layer of the streamwise turbulent flow. This approach is used for flows having planar surfaces, such as channel flow, and flows over curved surfaces, such as the interior of round pipes. However, surface curvature introduces an additional effect that can be significant, especially when the viscous region is not small compared to the pipe radius. The exact solutions for flow over transversely oscillating walls in a laminar pipe and planar channel flow are compared to the solution of Stokes’ second problem to determine the effects of wall curvature and/or finite domain size. It is shown that a single non-dimensional parameter, the Womersley number, can be used to scale these effects and that both effects become small at a Womersley number of greater than about 6.51, which is the Womersley number based on the thickness of the Stokes’ layer of the classical solution. 

Presented are vorticity statistics in drag reduced turbulent pipe flow at low and moderate Reynolds number. Drag reduction is achieved by transverse wall oscillations. Quantities of interest are the distributions of streamwise vorticity in the viscous and lower part of the buffer layer of the flow. We observe a sinusoidal pattern appearing in the distribution that is associated with the strengthening and weakening of counter-rotating vortex pairs. Presented alongside the phase varying distributions of vorticity are the phase averaged distribution of azimuthal and radial velocity fluctuations. The information presented provides a statistical evidence for the new proposed model for the near wall vortex distortion.