The analogy of singularities in direct methods for calculating steady three dimensional and unsteady two dimensional boundary layers: Analysis of reversed modes

The problem of occurrence of singularities in boundary layer equations, both in the unsteady two-dimensional and steady three-dimensional cases, is analytically studied by means of the global equations of momentum and entrainment. In the direct mode the velocity is given. It is shown that in opposition to the steady two-dimensional case, the occurrence of reversed flows does not generally create singularities, but indicates a downstream influence. In both cases, the analytical and numerical study shows that discontinuity lines can exist, corresponding to weak solutions of the equations, but these lines have no physical meaning. Particularly in the three-dimensional case they must not be confused with separation lines. The calculations in the inverse mode avoid any singularity. The velocity is then an unknown of the boundary layer problem. Such methods are useful to solve the coupling problem between viscid-inviscid flow and are also interesting to verify closure relations of calculation models in separated regions.