SINGULARITIES ENCOUNTERED IN 3-DIMENSIONAL BOUNDARY-LAYERS UNDER AN ADVERSE OR FAVORABLE PRESSURE-GRADIENT

Singularities in solutions of the classical boundary-layer equations a re considered, numerically and analytically, in an example of steady h ypersonic flow along a flat plate with three-dimensional surface rough ness. First, a wide parametric study of the breakdown of symmetry-plan e flow is performed for two particular cases of the surface geometry. Emphasis is put on the structural stability of the singularities' deve lopment to local/global variation of the pressure distribution. It is found that, as usual, the solution behaviour under an adverse pressure gradient involves the Goldstein- or marginal-type singularity at a po int of zero streamwise skin friction. As the main alternative, typical of configurations with favourable or zero pressure forcing, an invisc id breakdown in the middle of the flow is identified. Similarly to uns teady flows, the main features of the novel singularity include infini tely growing boundary-layer thickness and finite limiting values of th e skin-friction components. Subsequent analytical extensions of the si ngular symmetry-plane solution then suggest two different scenarios fo r the global boundary-layer behaviour: one implies inviscid breakdown of the flow at some singular line, the other describes the development of a boundary-layer collision at a downstream portion of the symmetry plane. In contrast with previous studies of the collision phenomenon in steady flows, the present theory suggests logarithmic growth of bou ndary-layer thickness on both sides of the discontinuity. Finally, an example of numerical solution of the full three-dimensional boundary l ayer equations is given. The flow regime chosen corresponds to invisci d breakdown of a centreplane flow under a favourable pressure gradient and development of the discontinuity/collision downstream. The numeri cal results near the origin of the discontinuity are found to be suppo rtive, producing quantitative agreement with the local analytical desc ription.