Evaluating Unsteady Forces in Turbulence-Modeled Flows from Vorticity and Reynolds Stress

Vortex force maps (VFMs) link vortical flow structures to aerodynamic forces through compact-domain integrals weighted by geometry-only Laplace potentials. Existing VFM demonstrations include inviscid, laminar, two-dimensional, and three-dimensional applications but cannot analyze turbulent flows unless fully resolved turbulent fields are available. Here, a method for predicting and attributing the turbulent force contribution from modeled turbulence fields is developed by deriving a Reynolds-averaged vortex force map (RA-VFM) directly from the incompressible Reynolds-averaged Navier–Stokes equations. The resulting decomposition augments the classical vortex-pressure (VP) term with a Reynolds-stress (RS) contribution, defined by the Laplace-kernel-weighted divergence of the modeled Reynolds stress. The RA-VFM is applied to a gliding Northern Goshawk (Accipiter gentilis) and an incidence-matched GOE803 airfoil section at [Formula: see text]. Dominant VP lift arises from spanwise vorticity, while dominant RS lift is associated with the z-component of the Reynolds-stress divergence. Both contributions can be obtained from snapshot data and are compacted within the RA-VFM kernel. RS is small for the quasi-two-dimensional airfoil outside deep stall but contributes strongly in separated and three-dimensional regimes. For the bird case, including RS reduces the reconstruction error to approximately 2% for lift and 1% for drag relative to CFD. The method improves interpretation and attribution of complex three-dimensional turbulent flows and may support some reduced-order models.