As the community investigates more complex flows with stronger streamwise variations and uses more physically inclusive stability techniques, such as BiGlobal theory, there is a perceived need for more accuracy in the base flows. To this end, the implication is that using these more advanced techniques, we are now including previously neglected terms of O(Re²). Two corresponding questions follow: (1) how much accuracy can one reasonably achieve from a given set of basic-state equations and (2) how much accuracy does one need to converge more advanced stability techniques? The purpose of this paper is to generate base flow solutions to successively higher levels of accuracy and assess how inaccuracies ultimately affect the stability results. Basic states are obtained from solving the self-similar boundary-layer equations, and stability analyses with LST, which both share O(1/Re) accuracy. This is the first step toward tackling the same problem for more complex basic states and more advanced stability theories. Detailed convergence analyses are performed, allowing to conclude on how numerical inaccuracies from the basic state ultimately propagate into the stability results for different numerical schemes and instability mechanisms at different Mach numbers.

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A combined experimental and numerical approach to the analysis of the secondary stability of realistic swept-wing boundary layers is presented. Global linear stability theory is applied to experimentally measured base flows. These base flows are three-dimensional laminar boundary layers subject to spanwise distortion due to the presence of primary stationary crossflow vortices. A full three-dimensional description of these flows is accessed through the use of tomographic particle image velocimetry (PIV). The stability analysis solves for the secondary high-frequency modes of type I and type II, ultimately responsible for turbulent breakdown. Several pertinent parameters arising from the application of the proposed methodology are investigated, including the mean flow ensemble size and the measurement domain extent. Extensive use is made of the decomposition of the eigensolutions into the terms of the Reynolds-Orr equation, allowing insight into the production and/or destruction of perturbations from various base flow features. Stability results demonstrate satisfactory convergence with respect to the mean flow ensemble size and are independent of the handling of the exterior of the measurement domain. The Reynolds-Orr analysis reveals a close relationship between the type I and type II instability modes with spanwise and wall-normal gradients of the base flow, respectively. The structural role of the in-plane velocity components in the perturbation growth, topology and sensitivity is identified. Using the developed framework, further insight is gained into the linear growth mechanisms and later stages of transition via the primary and secondary crossflow instabilities. Furthermore, the proposed methodology enables the extension and enhancement of the experimental measurement data to the pertinent instability eigenmodes. The present work is the first demonstration of the use of a measured base flow for stability analysis applied to the swept-wing boundary layer, directly avoiding the modelling of the primary vortices receptivity processes.

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Hairpin shaped Kelvin-Helmholtz waves are observed in tomographic PIV experiments on a micro-ramp wake. In this study, these waves are reproduced by applying BiGlobal stability theory to base flows conceived with the measurement data. The stability results converge with the number of instantaneous snapshots used for the base ow. The most unstable wavelength lies in the experimentally observed range and the flow structure closely resembles that shown in the snapshots.@en