The problem of laminar, incompressible flow over a periodic wavy surface is treated as a first-order perturbation to the boundary layer flow on a flat surface. The analysis demonstrates that some nonlinear terms in the disturbance boundary-layer equations are first order if the wave amplitude and disturbance sublayer thickness are comparable in magnitude. Further, the theory predicts that the nonlinear effects are confined to the thin sublayer adjacent to the wavy surface. Computer-generated, nonlinear solutions are presented for sinusoidal waves with a range of wave amplitudes, including cases with local separated flow regions.

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The previous analysis of laminar, incompressible flow over a periodic wavy surface is extended to include wavelengths which are large compared with the mean boundary-layer thickness. These larger wavelengths produce a stronger coupling between the outer inviscid flow and the viscous disturbance sublayer and, as a result, require the complete solution of the elliptic inviscid equations. The analysis is refined to allow for a net thickening of the mean boundary layer with increasing wave amplitude. Computer-generated solutions are presented for sinusoidal waves of varying amplitude and wavelength, including cases with local flow separation.

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