Transition theory and experimental comparisons on (I) amplification into streets and (II) a strongly nonlinear break-up criterion

Abstract

The two stages I, II are studied by using recent nonlinear theory and then compared with the experiments of Nishioka et al . (1979) on the transition of plane Poiseuille flow. The first stage I starts at low amplitude from warped input, which is deformed through weakly nonlinear interaction into a blow-up in amplitude and phase accompanied by spanwise focusing into streets. This leads into the strongly nonlinear stage II. It holds for a broad range of interactive boundary layers and related flows, to all of which the nonlinear break-up criterion applies. The experimental comparisons on I, II for channel flow overall show encouraging quantitative agreement, supporting recent comparisons (in the boundary-layer setting) of the description of stage I in Stewart & Smith (1992) with the experiments of Klebanoff & Tidstrom (1959) and of the break-up criterion of Smith (1988 a ) with the computations of Peridier et al (1991 a , b ).