Solitary-like waves in boundary-layer flows and their randomization

Abstract

Essentially nonlinear motions generated in incompressible boundary layers by external agencies are considered. A pertinent mathematical model for the Blasius flow is furnished by the forced Benjamin-Davis-Acrivos integral-differential equation. A steady hump is chosen as a simplest source in order to trace the disturbance-pattern evolution as the roughness height increases, provided that its length is kept fixed. Occurence of bifurcation phenomena features this problem; the first publication gives rise, in particular, to a specific regime with nearly limit-cycle-type oscillations in the immediate vicinity of the hump. After the second bifurcation studied, the nearly periodic regime collapses into irregular pulsations with erratic sequences of amplitudes and characteristic times. A brief discussion based on the forced Korteweg-de Vries equation lends credence to the view that the chaotically transitional process can be triggered at an earlier stage of wave amplification.