Nonlinear analysis of laminar boundary layer flow over a periodic wavy surface—Part II: Long waves

Abstract

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.