Effect of non-uniqueness and bifurcation in marginal separation theory

Speaker: Professor Stefan Braun, Institute of Fluid Mechanics and Heat Transfer, Vienna University of Technology.

Time: 4:00PM
Date: Thu 5th October 2006

Location: Mathematical Sciences Seminar Room

Viscous-inviscid interaction solutions for steady two-dimensional laminar high Reynolds number boundary layer flows featuring localized flow separation are known to exist up to a critical value G c of a controlling parameter G (e.g. angle of attack of a slender airfoil) only. The investigation of three-dimensional unsteady perturbations of such boundary layers in the near critical regime | G - G c| shows that the governing equations simplify significantly allowing (i) a systematic study of blow-up phenomena which are believed to indicate the onset of the fast transition process to turbulence and (ii) the optimization of control devices (suction, surface mounted obstacles) to increase or reduce G c (to delay or force transition). Specifically, it is found that the evolution of disturbances is described by a forced type of Fisher's equation known from mathematical biology and that its solutions leading to the formation of finite time singularities can be continued beyond the blow-up time thereby generating moving singularities which are interpreted as coherent vortical structures similar to those observed in experimental studies and direct numerical simulations of transitional separation bubbles.

(This talk is part of the Applied and Computational Mathematics series.)