Nonlinear analysis of laminar boundary layer flow over a periodic wavy surface

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.