Three-dimensional transverse instabilities in detached boundary layers

The direct numerical simulation of the incompressible Navier-Stokes equations of the flow above a bump shows a stationary longitudinal instability at a Reynolds number of Re = 400. A three-dimensional global mode linear analysis is used to interpret these results and shows that the most unstable eigenmode is steady and localized in the recirculation bubble, with spanwise wavelength of approximatively ten bump heights. An inviscid geometrical optics analysis along closed streamlines is then proposed and modified accordingly to account for viscous effects. This motivates a final discussion regarding the physical origin of the observed instability.