The nonlinear evolution of secondary instabilities in boundary layers

Abstract

Following the concepts of stability analysis, a study is made of the pre-breakdown stage of transition to turbulence in boundary layers. The first step consists of a ’decoupling’ of the primary and secondary instabilities. A perturbation method is used to solve for the primary wave, in the absence of any secondary disturbances. Once the wave is calculated, it is decomposed into a basic flow portion and an interaction portion. The basic flow portion acts as a parametric excitation for the secondary wave. The interaction portion then captures the resonance effects of the secondary back onto the primary. A perturbation method is also used for the secondary and interaction components. The results obtained are in three principal forms: Landau constants, amplitude growth curves, and velocity functions. While in good agreement with experiments and simulations, these results offer new explanations to the observed processes. In addition, a physically-based transition criteria is established.