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S. Braun, S. Scheichl, A. Kluwick:
"Adjoint operator approach in marginal separation theory";
Talk: 11th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM), Rodos Palace Hotel, Rhodes, GR; 09-21-2013 - 09-27-2013; in: "AIP Conference Proceedings", T.E. Simos et al. (ed.); American Institute of Physics, 1558 (2013), ISSN: 0094-243x; 261 - 264.

Thin airfoils are prone to localized flow separation at their leading edge if subjected to moderate angles of attack α. Although `laminar separation bubbles´ at first do not significantly alter the airfoil performance, they tend to `burst´ if α is increased further or perturbations acting upon the flow reach a certain intensity. This then leads either to global flow separation (stall) or triggers the laminar-turbulent transition process within the boundary layer flow. The present paper addresses the asymptotic analysis of the early stages of the latter phenomenon in the limit as the characteristic Reynolds number Re → ∞, commonly referred to as marginal separation theory (MST). A new approach based on the adjoint operator method is presented to derive the fundamental similarity laws of MST and to extend the analysis to higher order. Special emphasis is placed on the breakdown of the flow description, i.e. the formation of finite time singularities (a manifestation of the bursting process), and its resolution based on asymptotic reasoning. The computation of the spatio-temporal evolution of the flow in the subsequent triple deck stage is performed by means of a Chebyshev spectral method. The associated numerical treatment of fractional integrals characteristic of MST is based on barycentric Lagrange interpolation, which is described in detail.

viscous-inviscid interaction, triple deck theory, laminar separation bubble, laminar-turbulent transition, Chebyshev spectral

http://dx.doi.org/10.1063/1.4825471