Roughness-induced generation of crossflow vortices in three-dimensional boundary layers

The receptivity theory of Goldstein and Ruban is extended within the nonasymptotic (quasi-parallel) framework of Zavol'skii et al. to predict the roughness-induced generation of stationary and nonstationary instability waves in three-dimensional, incompressible boundary layers. The influence of acoustic-wave orientation, as well as that of different types of roughness geometries, including isolated roughness elements, periodic arrays, and two-dimensional lattices of compact roughness shapes, as well as random, but spatially homogeneous roughness distributions, is examined. The parametric study for the Falkner-Skan-Cooke family of boundary layers supports our earlier conjecture that the initial amplitudes of roughness-induced stationary vortices are likely to be significantly larger than the amplitudes of similarly induced nonstationary vortices in the presence of acoustic disturbances in the free stream. Maximum unsteady receptivity occurs when the acoustic velocity fluctuation is aligned with the wave-number vector of the unsteady vortex mode. On the other hand, roughness arrays that are oriented somewhere close to the group velocity direction are likely to produce higher instability amplitudes. Limitations of the nonasymptotic theory are discussed, and future work is suggested.