Subtleties in relating exact solutions of the differential equation of classical instability of the asymptoticsuction boundary layer to uniform asymptotic approximations therof
Abstract
I will use the abbreviation BMHR equation (for uc(Bussman,) Münz, Hughes & Reid) to denote the modified uc(OrrSommerfeld) equation that applies when the mean flow is the asymptotic suction boundary layer. uc(Dieter) Grohne (1950) and uc(Paul) Baldwin (1970) found several integral representations of exact solutions of the uc(OrrSommerfeld) and BMHR equations, respectively. In the mean time uc(W.D.) Lakin & W.H. Reid (1982) derived uniformlyvalid asymptotic solutions of the BMHR equation. Following uc(W.) Wasow (1953) they found it useful to define a family of seven canonical solutions (one of which is wellbalanced, three of which are balanced and three of which are dominantrecessive). As uc(Baldwin) pointed out in a 1985 paper the family of integral representations found by uc(Grohne) and uc(Baldwin,) though large enough to represent the general solution, does not immediately permit a onetoone correlation with seven solutions of uc(Lakin) & Reid. A careful correlation must enlarge the family of exact solutions given by uc(Grohne) and uc(Baldwin) and must, moreover, include suitable conformal transfomations between the planes of the uc(Langer) variable used by uc(Lakin) & Reid and the independent variable that arises most naturally in the exact integral representations. The present work addresses these problems.
 Publication:

APS Division of Fluid Dynamics Meeting Abstracts
 Pub Date:
 November 2003
 Bibcode:
 2003APS..DFD.DR010R