From Tracer Transport to Induced Drag: The Jones–Kusunose Gap as a Single-Station Diagnostic of Wingtip Vortices

<title>Abstract</title> <p> Wingtip vortices dominate the induced drag of every finite wing, yet the integral force measurements normally used to assess vortex-control devices report only the net penalty and reveal nothing about the mechanism a device employs. Different devices, such as blended winglets and spiroids, may reach similar span efficiency through different wake physics. This paper presents a single, uncertainty-propagating measurement chain that connects an individual tracer particle to the wing’s induced drag and resolves mechanism information inaccessible to direct force measurement. Time-resolved three-dimensional particle tracking velocimetry (Shake-the-Box, four cameras, 999 Hz) reconstructs the wake of a NACA 4416 half-span wing at a chord Reynolds number of 3.6 × 10 ⁵ . Particle trajectories are converted to an Eulerian velocity field, from which vorticity, Q-criterion cores, and Lamb–Oseen circulation and core-radius descriptors are extracted; the wake is then closed at the Trefftz plane by three independent integral methods (Maskell, Kusunose, Jones), with uncertainty propagated in closed form through every link. Applied to a baseline tip and three devices (split tip, blended winglet, spiroid), the difference between the full-wake Jones and compact-core Kusunose integrals—the Jones–Kusunose gap—acts as a single-station discriminator of drag-reduction mechanism: a near-zero gap denotes compact-core dominance; a large positive gap, core-rotation disruption with circulation redistributed into diffuse outer-wake vorticity; and a negative gap, a concentrated, intensified core. The three devices operate by three physically distinct mechanisms—span extension, core unwinding, and core intensification that share force-balance signatures but leave distinguishable vortex-topology fingerprints, using a single Trefftz-plane station and no far-field survey. </p>