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B. Scheichl: 
''Asymptotic theory of marginal turbulent separation''; 
Supervisor, Reviewer: A. Kluwick, H. Sockel; Institute of Fluid Mechanics and Heat Transfer (E322), Vienna University of Technology, Vienna, Austria, 2001.

@phdthesis{scheichl01[TUW-160649],
    author = {Scheichl, Bernhard},
    title = {Asymptotic theory of marginal turbulent separation},
    school = {Institute of Fluid Mechanics and Heat Transfer (E322), Vienna University of Technology, Vienna, Austria},
    year = {2001},
    url = {http://publik.tuwien.ac.at/files/pub-mb_1930.pdf},
    abstract = {The development of an asymptotic theory of turbulent separation has been hampered severely by the fact that a pressure increase of {{\$}O}(1){\$} appears to be necessary to separate an initially firmly attached turbulent boundary layer, even in the limit of infinite Reynolds number, denoted by {{\$}{\textbackslash}Rey{\$}}. According to classical theory, the latter one is characterized by a small velocity defect with respect to the external irrotational flow. A different situation is expected to arise if one considers boundary layers subjected to adverse pressure gradients such that the wall shear stress vanishes eventually but immediately recovers. Similar to the case of laminar marginally separated flows, the pressure changes in the vicinity of the point of vanishing wall shear then are small. But then the difficulty is encountered that separation is not compatible with a small velocity defect but rather requires the existence of a defect of {{\$}O}(1){\$}. Thus, separation is seen to be associated with the appearance of a nonlinear wake-like solution describing the outer part of the boundary layer, whose slenderness then is determined by an additional small parameter which is essentially independent of {{\$}{\textbackslash}Rey{\$}}. This allows for further analytical progress which suggests a self-consistent description of the separation process and, among others, shows how the classical logarithmic law of the wall is gradually transformed into the well-known square root law that holds at the point of zero skin friction. Supported by numerical calculations, the important result is found, among others, that separation is accompanied by a regular solution of the inviscid wake. It gives rise to a small reverse-flow regime in the limit {{\$}{\textbackslash}Rey{\^}{\{}}-1{\}}=0{\$} within the framework of pure boundary layer theory, strikingly contrasting the singular behaviour known from its laminar counterpart. Moreover, in the special case of quasi-equilibrium flows characterized by an only weakly varying Rotta--Clauser parameter {\$}{\textbackslash}beta{\$} the transition from the classical defect to the nonlinear wake is found to be associated with non-uniqueness of the\par
solutions in the case {\$}{\textbackslash}beta{\textbackslash}to{\textbackslash}infty{\$}. The analysis presented is essentially independent of the choice of a specific closure for the Reynolds shear stress.}
}