Skin-Friction and Surface-Pressure Structures in Near-Wall Flows

Skin-friction and surface-pressure in a viscous flow constitute a pair of the intrinsically coupled physical quantities denoted by the notation (, ), which determines the near-wall flow structures. The exact (, ) relation derived from the Navier–Stokes (NS) equations provides a rational foundation for reconstruction of the (, ) structures in complex flows. Based on this coupling relation, a field can be obtained from the perturbed field for the given boundary enstrophy flux field of a base flow as an inverse problem in the first-order approximation. Then, the corresponding near-wall velocity field is reconstructed by using the Taylor-series-expansion solution of the NS equations. Some elemental and complex (, ) structures in three-dimensional flow separations are reconstructed to demonstrate the applicability of the proposed method.