Wave-envelope steepening in the Blasius boundary-layer

• Published in: European journal of mechanics, B, Fluids B, Fluids, 2000-11, Vol.19 (6), p.871-888
• Main Author: Healey, Jonathan J.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Laminar boundary layers; Laminar flows; Physics; Stability of laminar flows
• ISSN: 0997-7546; 1873-7390
• DOI: 10.1016/S0997-7546(00)01110-9

Previous experiments into the evolution of small amplitude disturbances to the Blasius boundary layer have shown that modulated waves become nonlinear at lower amplitudes than unmodulated waves. In this paper we propose a mechanism that may account for this behaviour. It involves a wave-envelope steepening scenario analogous to water-wave overturning and shock formation. Larger amplitude parts of a modulated wave travel at a different speed to lower amplitude parts, due to the proposed nonlinear mechanism, leading to an asymmetry between the steepness of decaying and growing sections. These effects occur in the higher order Ginzburg–Landau equation, so this may be a useful model for the process. Results from a windtunnel experiment, and a direct numerical simulation, will be presented and analysed for this effect. Both show a clear progressive asymmetry developing as the amplitude, and hence nonlinearity, are increased. Comparison between the experiment and simulation highlights key differences between two- and three-dimensional nonlinear evolutions.