Receptivity of a swept-wing boundary layer to micron-sized discrete roughness elements

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.