Jm. Hoyle et Ft. Smith, ON FINITE-TIME BREAK-UP IN 3-DIMENSIONAL UNSTEADY INTERACTING BOUNDARY-LAYERS, Proceedings - Royal Society. Mathematical and physical sciences, 447(1931), 1994, pp. 467-492
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.