Receptivity mechanisms in three-dimensional boundary-layer flows

Authors: Schrader, L.-U., Brandt, L.B., Henningson, D.S.H.
Document Type: Article
Pubstate: Published
Journal: J. Fluid Mech.
Volume: 618   209-241
Year: 2009


Receptivity in three-dimensional boundary-layer flow to localized surface roughness and free-stream vorticity is studied. The Falkner-Skan-Cooke boundary layer subject to a favorable pressure gradient is considered to model the flow slightly downstream of a swept-wing leading edge. In this region stationary and travelling cross-flow instability dominates over other instability types. Three scenarios are investigated: the presence of low-amplitude chordwise localized, spanwise periodic roughness elements on the plate, the impingement of a weak vortical free-stream mode on the boundary layer and the combination of both disturbance sources.

Three receptivity mechanisms are identified: steady receptivity to roughness, unsteady receptivity to free-stream vorticity and unsteady receptivity to vortical modes scattered at the roughness. Both roughness and vortical modes provide efficient linear receptivity mechanisms for stationary and travelling cross-flow instabilities. We find that stationary cross-flow modes dominate for low-level free-stream turbulence, whereas higher turbulence levels will promote the unsteady receptivity mechanism. Under the assumption of small amplitudes of the roughness and the free-stream disturbance, the unsteady receptivity process due to scattering of free-stream vorticity at the roughness has been found to give small initial disturbance amplitudes in comparison to the linear mechanism for free-stream modes. However, in many environments free-stream vorticity and roughness may excite interacting unstable stationary and travelling cross-flow waves. This nonlinear process may rapidly lead to large disturbance amplitudes and promote transition to turbulence.