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B. Scheichl, A. Kluwick: 
''Non-unique turbulent boundary layer flows having a moderately large velocity defect: a rational extension of the classical asymptotic theory''; 
Theoretical and Computational Fluid Dynamics, 27 (2013), 6; 735 - 766.

@article{scheichl13:735[TUW-188516],
    author = {Scheichl, Bernhard and Kluwick, Alfred},
    title = {Non-unique turbulent boundary layer flows having a moderately large velocity defect: a rational extension of the classical asymptotic theory},
    journal = {Theoretical and Computational Fluid Dynamics},
    year = {2013},
    volume = {27},
    number = {6},
    pages = {735--766},
    url = {http://publik.tuwien.ac.at/files/PubDat_188516.pdf},
    doi = {10.1007/s00162-012-0266-x},
    keywords = {Matched asymptotic expansions, Boundary layer theory, Turbulence},
    abstract = {The classical analysis of turbulent boundary layers in the limit of large Reynolds number Re is characterised by an asymptotically small velocity defect with respect to the external irrotational flow. As an extension of the classical theory, it is shown in the present work that the defect may become moderately large and, in the most general case, independent of Re but still remain small compared to the external streamwise velocity for non-zero pressure gradient boundary layers. That wake-type flow turns out to be characterised by large values of the Rotta--Clauser parameter, serving as an appropriate measure for the defect and hence as a second perturbation parameter besides Re. Most importantly, it is demonstrated that also this case can be addressed by rigorous asymptotic analysis, which is essentially independent of the choice of a specific Reynolds stress closure. As a salient result of this procedure, transition from the classical small-defect to a pronounced wake flow is found to be accompanied by quasi-equilibrium flow, described by a distinguished limit that involves the wall shear stress. This situation is associated with double-valued solutions of the boundary layer equations and an unconventional weak Re-dependence of the external bulk flow -- a phenomenon seen to agree well with previous semi-empirical studies and early experimental observations. Numerical computations of the boundary layer flow for various values of Re reproduce these analytical findings with satisfactory agreement.}
}



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