On Secondary Instabilities in Boundary Layers

Abstract

One of the routes to transition consists of a cascade of successive instabilities. The first instability is usually called primary instability and it may consist of a two- or three-dimensional Tollmien Schlichting wave, a Gortler vortex, or a crossflow instability. The next two instabilities in the cascade are usually called secondary and tertiary instabilities. Two approaches of treating secondary instability are reviewed and compared. The first approach is a mutual interaction approach which accounts for the influence of the secondary instability on the primary instability. The second approach is usually called parametric instability. It does not account for this influence and leads to linear equations with periodic or quasi-periodic coefficients. Whereas the mutual interaction approach is not limited by the amplitude of the secondary instability, the parametric approach is limited to infinitesimal amplitudes of the secondary instability. The role of the Squire mode in the secondary instability on a flat plate is discussed.