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Publications in Scientific Journals:

S. Braun, A. Kluwick:
"Unsteady three-dimensional marginal separation caused by surface mounted obstacles and/or local suction";
Journal of Fluid Mechanics, 514 (2004), 121 - 152.



English abstract:
Earlier investigations of steady two-dimensional marginally separated laminar boundary layers have shown that the non-dimensional wall hear (or equivalently the negative non-dimensional perturbation displacement thickness) is governed by a nonlinear integro-differential equation. This equation contains a single controlling parameter Gamma characterizing, for example, the angle of
attack of a slender airfoil and has the important property that (real) solutions exist up to a critical value Gamma_c of Gamma only.
Here we investigate three-dimensional unsteady perturbations of an
incompressible steady two-dimensional marginally separated laminar boundary layer with special emphasis on the flow behaviour near Gamma_c. Specifically, it is shown that the integro-differential equation which governs these disturbances if Gamma_c-Gamma=O(1) reduces to a nonlinear partial differential equation - known as Fisher equation - as Gamma approaches the critical value Gamma_c.
This in turn leads to a significant simplification of the problem allowing,among other things, a systematic study of devices used in boundary layer control and an analytical investigation of the conditions leading to the formation of finite time singularities which have been observed in earlier numerical studies of unsteady two-dimensional and three-dimensional flows in the vicinity of a line of symmetry. Also it is found possible to construct exact solutions which describe waves of constant form travelling in the spanwise direction. These waves may contain singularities which can be interpreted as vortex sheets. The existence of these solutions strongly suggests that solutions of the Fisher equation which lead to finite time blow-up may be extended beyond the blow-up time thereby
generating moving singularities which can be interpreted as vortical structures qualitatively similar to those emerging in direct numerical simulations of near critical (i.e. transitional) laminar separation bubbles. This is supported by asymptotic analysis.


"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1017/S0022112004000187

Online library catalogue of the TU Vienna:
http://aleph.ub.tuwien.ac.at/F?base=tuw01&func=find-c&ccl_term=AC04968724

Electronic version of the publication:
http://journals.cambridge.org/action/displayIssue?jid=FLM&volumeId=514&issueId=-1


Created from the Publication Database of the Vienna University of Technology.