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Propagation of stationary and traveling waves in a leading-edge boundary layer of a swept wing

The transition characteristics around the leading edge of a swept-back wing shape were numerically investigated. We conducted direct numerical simulations (DNSs) of a swept-wing shape with a high Reynolds number Re=Rec/cos Λ=5.85×106 based on the chord length with a sweep angle Λ=70°. In the study, a randomly distributed impulsive local body force was applied at the wall to encourage a transition. Through impulsive local forcing, two coherent waves formed in both an attachment line and a three-dimensional boundary layer: A stationary elongated streak structure in the external flow direction and a traveling wave in the sweep direction. These characteristics in the attachment line were slightly different from those in the three-dimensional boundary layer. We computed the nonmodal transient energy growth for the present leading-edge boundary layer and compared the coherent waves observed in the DNSs. The stationary and traveling modes in the DNSs are found to be in a transient growth group; these modes temporally grow to the maximum in the short target time ( τ<0.02). One of our conclusions is that both waves occurring in the present attachment line are strongly related to the short-term transient energy growth phenomena of the nonorthogonality of the flow field. When the roughness forcing was gradually increased, the traveling wave was not generated, whereas the stationary wave was. This was considered because the present attachment-line boundary layer was receptive to a small disturbance and more likely to generate a stationary wave than a traveling wave.