The Stokes boundary layer for a power-law fluid

► Self-similar solutions for oscillatory boundary-layer flow of a power-law fluid. ► For shear-thickening fluids, the boundary layer is of finite thickness. ► For shear-thinning fluids, oscillations decay algebraically away from the wall. ► Velocity and shear stress vary non-sinusoidally with time. ► Numerical integration confirms that these solutions are attracting.