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The receptivity of a laminar boundary layer flow to small amplitude wallroughness is investigated on an ONERA-D swept aerofoil by introducing adedicated resolvent operator based on linearised small amplitude walldisplacements. The singular value decomposition of this operator for a givenspanwise wavenumber provides optimal wall roughness and flow responses thatmaximise an input-output gain. At the most receptive spanwise wavenumber, theoptimal response is a cross-flow mode associated with an optimal roughnesslocated close to the attachment-line and presenting a wavy shape with awavevector nearly orthogonal to the external streamlines. The method thereforeallows direct identification of the location and structure (chordwise andspanwise wavenumbers) of the most receptive roughness. For various given wallroughness shapes and locations (periodic or compact in the chordwise and/orspanwise directions), an approximation of the response based on the dominantoptimal response is shown to accurately match the total response downstream ofthe roughness. The method therefore allows a straightforward computation of theresponse of the flow to any given small amplitude roughness.

Receptivity of swept-aerofoil flows to small amplitude wall roughness using resolvent analysis based on wall displacement