We analyse the three-dimensional non-parallel instability mechanisms responsible for transition to turbulence in regions of recirculating steady laminar two-dimensional incompressible separation bubble ®ow in a twofold manner. First, we revisit the problem of Tollmien{Schlichting (TS)-like disturbances and we demonstrate, for the rst time for this type of ®ow, excellent agreement between the parabolized stability equation results and those of independently performed direct numerical simulations. Second, we perform a partial-derivative eigenvalue problem stability analysis by discretizing the two spatial directions on which the basic ®ow depends, precluding TS-like waves from entering the calculation domain. A new two-dimensional set of global ampli ed instability modes is thus discovered. In order to prove earlier topological conjectures about the ®ow structural changes occurring prior to the onset of bubble unsteadiness, we reconstruct the total ®ow eld by linear superposition of the steady two-dimensional basic ®ow and the new most-ampli ed global eigenmodes. In the parameter range investigated, the result is a bifurcation into a three-dimensional ®ow eld in which the separation line remains una¬ected while the primary reattachment line becomes three dimensional, in line with the analogous result of a multitude of experimental observations.

Revisiting the classical acoustics problem of rectangular side-branch cavities in a two-dimensional duct of infinite length, we use the finite-element method to numerically compute the acoustic resonances as well as the sound transmission and reflection for an incoming fundamental duct mode. To satisfy the requirement of outgoing waves in the far field, we use two different forms of absorbing boundary conditions, namely the complex scaling method and the Hardy space method. In general, the resonances are damped due to radiation losses, but there also exist various types of localized trapped modes with nominally zero radiation loss. The most common type of trapped mode is antisymmetric about the duct axis and becomes quasi-trapped with very low damping if the symmetry about the duct axis is broken. In this case a Fano resonance results, with resonance and antiresonance features and drastic changes in the sound transmission and reflection coefficients. Two other types of trapped modes, termed embedded trapped modes, result from the interaction of neighbouring modes or Fabry–Pérot interference in multi-cavity systems. These embedded trapped modes occur only for very particular geometry parameters and frequencies and become highly localized quasi-trapped modes as soon as the geometry is perturbed. We show that all three types of trapped modes are possible in duct–cavity systems and that embedded trapped modes continue to exist when a cavity is moved off centre. If several cavities interact, the single-cavity trapped mode splits into several trapped supermodes, which might be useful for the design of low-frequency acoustic filters.

An open system or open resonator is a domain of wave activity separated from the exterior by a partly open or partly transparent surface. Such open resonators lose energy to infinity through radiation. The numerical computation of the corresponding resonances is complicated by spurious reflections of the outgoing waves at the necessarily finite grid boundaries. These reflections can be reduced to extremely low levels by applying perfectly matched layer (PML) absorbing boundary conditions, which separate the discrete resonances from the continuous spectrum. Using a simple one-dimensional model problem, the influence of the various PML parameters is determined by a numerical error analysis. In addition to one-dimensional open resonators, two-dimensional open resonators as well as various resonating structures in waveguides are considered, and the resonant spectra and selected modes are evaluated. For the first time, leaky modes are computed for several resonating structures in a waveguide in addition to the trapped modes published in the literature. In applications, leaky mode resonances are often more important than trapped mode resonances. Gap tones, observed in a model problem of high-lift configurations, are identified as transversal resonant modes with the lowest radiation losses.

The influence of the streamwise pressure gradient and a nonadiabatic surface on boundary layer transition was experimentally investigated at the Cryogenic Ludwieg-Tube Göttingen, Germany. Boundary layer transition was detected nonintrusively by means of the temperature-sensitive paint technique. The wind-tunnel model was designed to achieve a quasi-uniform streamwise pressure gradient over a large portion of the model chord length. This allowed the effects on boundary layer transition of the streamwise pressure gradient and wall temperature ratio to be decoupled. The model was tested at high Reynolds numbers and at a high subsonic Mach number. Favorable, almostzero, and adverse streamwise pressure gradients were considered; and various temperature differences between the flow and the model surface were implemented. Stronger flow acceleration and lower wall temperature ratios led to an increase of the transition Reynolds number. Larger increases in the transition Reynolds number were obtained at more pronounced flow acceleration for the same reduction in the wall temperature ratio. The measured pressure distributions served as input for boundary layer stability computations, performed according to compressible, linear, local stability theory under the (quasi-) parallel-flow assumption. Amplification factors of the Tollmien-Schlichting waves were shown to be reduced by stronger favorable pressure gradients and lower wall temperature ratios, which was in agreement with the observed variation in the transition Reynolds number.

Surface pressure-sensors have been used to measure the second-mode boundary layer instability on a 7• half-angle sharp cone at zero angle of attack in the quiet Mach-6 wind tunnel at Purdue and in the conventional Mach-6 wind tunnel in Braunschweig. The measurements were made using a stream-wise array of high-frequency sensors. They show the second-mode waves in quiet and noisy flow at different unit Reynolds numbers. The quiet flow data is compared to results in noisy flow. The signal quality allows for the calculation of amplification rates, which are compared to the results of linear stability computations.