Reply to 0.R. Burggraf

Abstract

Now suppose the second order term of the outer expansion is known. Then the normal velocity near the surface can be calculated from the Taylor seriesIn particular, at y = A* we findwhich, together with (11), leads to Fannelop's result. Similarly, at y = d we findwhich is just the formula of Li and Gross. From the preceding analysis, we have three possible boundary conditions, all equivalent, to apply to the second order term of the outer expansion :1) The stream function or effective blowing velocity at the surface, given by (8), (10), or (11). This condition is the most straightforward to apply in weak interaction theory, and is the accepted version by most practitioners of the method of inner and outer expansions.2) The stream function vanishing on an effective displacement surface, as suggested by Fannelop. This procedure has the drawback that the solution is needed for y < A* to continue with the second order boundary-layer term, as evidenced by (5) . If only the second order outer solution is needed, this approach may be advantageous.3) The flow angle at the outer edge of the boundary layer, as given by Li and Gross. This procedure has the same drawback as item 2, but appears to be natural for strong interaction problems. In that case, of course, the method of inner and outer expansions is not applicable in the form developed here.