ON FINITE-TIME BREAK-UP IN 3-DIMENSIONAL UNSTEADY INTERACTING BOUNDARY-LAYERS

The occurrence of finite-time break-up singularities in nonlinear inte ractive boundary layers is investigated for three-dimensional unsteady motions, extending previous two-dimensional theory. This is with a vi ew to linking with experimental observations of hairpin vortices and t he like in transitional and turbulent boundary layers. Particular case s of three-dimensional interaction are tackled first, in which locally the normalized pressure and displacement remain comparable, two main contexts being for liquid-layer flow at subcritical Froude numbers and sublayer flow over relatively short steep humps. More general interac tions are then considered afterwards. Computational and analytical pro perties are studied, with special interest in the mixed elliptic-hyper bolic type of the partial-differential equation for the local pressure at break-up. The main theoretical and practical consequences are also addressed.