SHORT-SCALE BREAK-UP IN UNSTEADY INTERACTIVE LAYERS - LOCAL DEVELOPMENT OF NORMAL-PRESSURE GRADIENTS AND VORTEX WIND-UP

Following the finite-time collapse of an unsteady interacting boundary layer (step 1), shortened length and time scales are examined here in the near-wall dynamics of transitional-turbulent boundary layers or d uring dynamic stall. The next two steps are described, in which (step 2) normal pressure gradients come into operation along with a continui ng nonlinear critical-layer jump and then (step 3) vortex formation is induced typically. Normal pressure gradients enter in at least two wa ys, depending on the internal or external flow configuration. This yie lds for certain internal flows an extended KdV equation with an extra nonlinear integral contribution multiplied by a coefficient which is p roportional to the normal rate of change of curvature of the velocity profile locally and whose sign turns out to be crucial. Positive value s of the coefficient lead to a further finite-time singularity, while negative values produce a rapid secondary instability phenomenon. Zero values in contrast allow an interplay between solitary waves and wave packets to emerge at large scaled times, this interplay eventually re turning the flow to its original, longer, interactive, boundary-layer scales but now coupled with multiple shorter-scale Euler regions. In e xternal or quasi-external flows more generally an extended Benjamin-On e equation holds instead, leading to a reversal in the roles of positi ve and negative values of the coefficient. The next step, 3, typically involves the strong wind-up of a local vortex, leading on to explosio n or implosion of the vortex. Further discussion is also presented, in cluding the three-dimensional setting, the computational implications, and experimental links.