ABSTRACT
Analogous expressions can be derived fort < x. These asymptotic forms reveal the existence of a boundary layer of thickness ,\ -l at x = 0 ( cf. the remark at the end of Section 3) and can be rendered still simpler, within the layer and without, when exponentially small terms are ignored. Thus, in the layer, where the appropriate spatial coordinate is e =AX, one obtains
1 1 ( 1-t ) P'"" - .\t ln(1-t), U '"" -.\tIn 1 _te-e , (39)
(43)
1 1 1 P"' ".\InA-".\ln(s-so), U"' ".\ln{1 + TJ/(s-so)}, (45)
thereby completing the solution in the sublayer. Observe that the sublayer has a locally self-similar structure and that the similarity variable TJ/(s-s0 ) represents a continuous shrinkage of the region in which </> assumes values higher than any fixed fraction of its maximum.
