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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 …