A hierarchy of low-dimensional Galerkin models is proposed for the viscous, incompressible flow around a circular cylinder building on the pioneering works of Stuart (1958), Deane et al. (1991), and Ma & Karniadakis (2002). The empirical Galerkin model is based on an eight-dimensional Karhunen-Loève decomposition of a numerical simulation and incorporates a new 'shift-mode' representing the mean-field correction. The inclusion of the shift-mode significantly improves the resolution of the transient dynamics from the onset of vortex shedding to the periodic von Kármán vortex street. In addition, the Reynolds-number dependence of the flow can be described with good accuracy. The inclusion of stability eigenmodes further enhances the accuracy of fluctuation dynamics. Mathematical and physical system reduction approaches lead to invariant-manifold and to mean-field models, respectively. The corresponding two-dimensional dynamical systems are further reduced to the Landau amplitude equation.

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Separation control is an important issue in the physiology of birdflight. Here, the adaption of the separation control mechanism by bird feathers to the requirements of engineering applications is described in detail. Self-activated movable flaps similar to artificial bird feathers represent a high-lift system for increasing the maximum lift of airfoils. Their effect on the unsteady flow around a two-dimensional airfoil configuration is investigated by a joint numerical and experimental study. First, attention is paid to the automatic opening and closing mechanism of the flap. Following this, its beneficial effect on lift is investigated for varying incidences and flap configurations. In-depth analysis of experimental and numerical results provides a detailed description of the important phenomena and the effect of self-adjusting flaps on the flow around the airfoil. In the second part of this paper, a contribution is made to verification of the applicability of unsteady Reynolds-averaged approaches using statistical turbulence models for unsteady flows with particular attention to turbulent time scales with comparison to the results of a hybrid simulation based on unsteady Reynolds-averaged Navier-Stokes equations and large-eddy simulation. Finally, flight experiments are described using an aircraft with movable flaps fitted on its laminar wing. Nomenclature A = amplitude of oscillation b = wing span c = chord length c F = flap-moment coefficient c G = gravity-moment coefficient c L ; c D = lift and drag coefficients c R = reverse flow parameter k = turbulent kinetic energy Lt = turbulent length scale l F = flap length M F = flap moment due to fluid force M G = flap moment due to gravity Re = Reynolds number based on chord length Sr = Strouhal number based on flap length u 0 = inflow velocity x d = detachment position = angle of attack , max = flap deflection angle, maximum angle = conventional flap angle = density ! = specific turbulent dissipation

We present two novel approaches to improve the behaviour of DES in the region where an attached boundary layer (handled with RANS) flows into a separated shear layer (to be resolved using LES). The approaches aim to be generally-applicable and retain the non-zonal nature of DES. Furthermore, the formulations are local and can be readily implemented in general-purpose solvers. One approach introduces an adaptive grid scale definition, sensitised to the local vorticity orientation. The second approach, which can be combined with the first, involves the incorporation of alternative SGS model formulations that discern between quasi 2D and developed 3D flow states. Both modifications lead to a strong reduction of eddy viscosity in the early shear layer. Consequently, a significant acceleration of RANS to LES transition is demonstrated for a plane shear layer, a backwards-facing step and a round jet, with results from two different flow solvers shown. The greatest improvement is seen when the approaches are applied in combination.

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The time-domain impedance boundary conditions of Tam and Auriault are extended for impedance boundaries with subsonic mean flows. This extension requires an effective impedance. A model for the effective impedance is proposed, which guarantees the continuity of particle displacement over an infinitely thin shear layer connecting the fluid to the impedance boundary as described by Myers. Together with the effective impedance model, the time domain impedance boundary condition renders the requirement of measuring the effective impedance under flow conditions unnecessary. To demonstrate the feasibility of the extended boundary conditions, a numerical validation using the NASA Grazing Incidence Tube measurements of Jones et al. is carried out. The assumed velocity on the infinitely thin shear layer connecting the flow over the surface to the locally reacting wall is shown to have a strong influence on the performance of the liner. Another important parameter identified is the shape of the mean flow profile, which not only causes convective effects but also may excite possible flow instabilities. It is demonstrated that satisfactory results can be obtained using the extended time domain impedance boundary condition based on the correct effective impedances and mean flow profiles.