Solutions of multi-dimensional initial-value and eigenvalue problems that govern linear instability of flow in the vicinity of laminar separation bubbles forming in boundary layers from incompressible to hypersonic flow have permitted placing knowledge gained from simplified local analyses on a firmer theoretical footing and revealed physical mechanisms of separated flow instability inaccessible to classic linear theory. The first part of the talk will discuss the footprints of the dominant stationary and traveling primary and secondary global eigenmodes as well as linear optimal disturbances of spanwise homogeneous incompressible laminar separated flows over wings and low pressure turbine blades. Results will be contrasted against recently obtained linear global modes on finite aspect ratio swept wings. In the second part of the talk, the laminar separation bubble formed at a compression corner in supersonic flow will be shown to sustain linear instabilities in which the recompression shock forms an integral part of the amplitude functions of the dominant global modes, a result which renders questionable instability analyses in which shocks (or their effects) are neglected. An analogous conclusion is reached in shock-induced laminar separation bubble in hypersonic flow over double cones and double wedges, where both two- and three-dimensional global instability analysis has shown the intimate connection (through the global mode amplitude functions) of instability in the laminar separation zone, the triple point, the slip line and the shock system downstream of the laminar separation bubble.
