The effects of a spanwise row of finite-size cylindrical roughness elements in a laminar, compressible, three-dimensional boundary layer on a wing profile are investigated by direct numerical simulations (DNS). Large elements are capable of immediately tripping turbulent flow by either a strong, purely convective or an absolute/global instability in the near wake. First we focus on an understanding of the steady near-field past a finite-size roughness element in the swept-wing flow, comparing it to a respective case in unswept flow. Then, the mechanisms leading to immediate turbulence tripping are elaborated by gradually increasing the roughness height and varying the disturbance background level. The quasi-critical roughness Reynolds number above which turbulence sets in rapidly is found to be Re kk,qcrit ≈ 560 and global instability is found only for values well above 600 using nonlinear DNS; therefore the values do not differ significantly from two-dimensional boundary layers if the full velocity vector at the roughness height is taken to build Re kk . A detailed simulation study of elements in the critical range indicates a changeover from a purely convective to a global instability near the critical height. Finally, we perform a three-dimensional global stability analysis of the flow field to gain insight into the early stages of the temporal disturbance growth in the quasi-critical and over-critical cases, starting from a steady state enforced by damping of unsteady disturbances.

The receptivity of a laminar swept-wing boundary layer to a spanwise array of circular roughness elements is investigated by means of direct numerical simulations (DNS). The initial amplitude of a steady crossflow mode generated by the shallow roughness elements does not vary strictly linearly with the roughness height, as often assumed. Rather, a fundamental, superlinear dependence of the receptivity amplitude on the roughness height is found. In order to account for shape effects, the roughness geometry is Fourier decomposed to its spanwise spectral content, and elements with a reduced spectrum are investigated. If only modes are present that synthesise a regular structure of alternating bumps and dimples of equal shape and size, the receptivity amplitude is strictly linear for each mode and nominal roughness heights up to at least 15 % of the local displacement thickness.

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Turbulent mixing layers emanating from slanted trailing edges or nozzles evolve in a manner that is explainable by applying the independence principle to boundary layer flows. Although measurements downstream of a planar chevron splitter plate validate the concept, the intent of this short article is to re-examine the broader ramifications of this observation. Turbulent boundary layer growth on a yawed flat plate is re-examined as is the attached flow direction near the trailing edge of a highly swept-back wing.