THEORETICAL ASPECTS OF TRANSITION AND TURBULENCE IN BOUNDARY-LAYERS

The main points of recent theoretical and computational studies on bou ndary-layer transition and turbulence are highlighted. The work is bas ed on high Reynolds numbers and attention is drawn to nonlinear intera ctions, breakdowns, and scales. The article focuses in particular on t ruly nonlinear theories for which the mean-flow profile is completely altered from its original state. There appear to be three such theorie s, dealing with 1) nonlinear pressure-displacement interactions, 2) vo rtex/wave interactions, and 3) Euler-scale flows. Specific recent find ings noted for these three, and in quantitative agreement with experim ents, are the following. 1) Nonlinear finite-time breakups occur in un steady interactive boundary layers, leading to sublayer eruption and v ortex formation; here the theory agrees with experiments on the occurr ence of the first spike. 2) Vortex/wave interactions give rise to fini te-distance blowup of displacement thickness, then interaction and bre akup (as ''in 1''); this theory agrees with experiments on the formati on of three-dimensional streets. 3) The Euler-scale and related theori es lead to the prediction of turbulent boundary-layer microscale, disp lacement- and stress-sublayer thicknesses.