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Three-dimensional transverse instabilities in detached boundary layers. (English) Zbl 1105.76028
Summary: A direct numerical simulation of incompressible Navier–Stokes equations of the flow over a bump shows a stationary longitudinal instability at a Reynolds number of \(Re\,{=}\,400\). Here we use a three-dimensional global mode linear analysis to interpret these results and show that the most unstable eigenmode is steady and localized in the recirculation bubble, with spanwise wavelength of approximately ten bump heights. An inviscid geometrical optics analysis along closed streamlines is then proposed and modified to account for viscous effects. This motivates a final discussion regarding the physical origin of the observed instability.

MSC:
76E09 Stability and instability of nonparallel flows in hydrodynamic stability
76D05 Navier-Stokes equations for incompressible viscous fluids
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
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