Discrete linear local eigenmodes in a separating laminar boundary layer

Abstract

AbstractThe evolution of two- and three-dimensional small-amplitude disturbances in the laminar part of a laminar separation bubble is investigated in detail. We apply a combination of local linear stability theory, results from different experimental measurement campaigns and direct numerical simulations to identify two different discrete eigenmodes in the laminar part of the bubble. A stable eigenmode, the outer mode, governs unsteady oscillations in the upstream part of the bubble. However, this perturbation is quickly overtaken by an unstable eigenmode, the inner mode, which eventually leads to transition of the detached shear layer. Such a behaviour is observed due to an acceleration region with a favourable pressure gradient preceding the adverse-pressure-gradient region. The flow is stable in the acceleration region, in which the outer mode is only moderately damped, while the inner mode is strongly damped. At the onset of instability for the unstable eigenmode upstream of separation, both viscous Tollmien–Schlichting and inviscid Kelvin–Helmholtz instability mechanisms contribute to amplification, while deeper inside the bubble only the inviscid mechanism is active. If the explicit forcing is moved to a region downstream of the favourable pressure gradient, only the unstable eigenmode appears. The same behaviour is found for two-dimensional and weakly oblique waves.