We employ experiments to study aspect ratio (A) effects on the vortex structure, circulation and lift force for flat-plate wings rotating from rest at 45 • angle of attack, which represents a simplified hovering-wing half-stroke. We use the time-varying, volumetric A = 2 data of Carr et al. (Exp. Fluids, vol. 54, 2013, pp. 1-26), reconstructed from phase-locked, phase-averaged stereoscopic digital particle image velocimetry (S-DPIV), and an A = 4 volumetric data set matching the span-based Reynolds number (Re) of A = 2. For A = 1-4 and Re span of O(10 3 -10 4 ), we directly measure the lift force. The total leading-edge-region circulation for A = 2 and 4 compares best overall using a span-based normalization and for matching rotation angles. The total circulation increases across the span to the tip region, and is larger for A = 2. After the startup, the total circulation for each A has a similar slope and a slow growth. The first leading-edge vortex (LEV) and the tip vortex (TV) for A = 4 move past the trailing edge, followed by substantial breakdown. For A = 2 the outboard, aft-tilted LEV merges with the TV and resides over the tip, although breakdown also occurs. Where the LEV is 'stable' inboard, its circulation saturates for A = 2 and the growth slows for A = 4. Aft LEV tilting reduces the spanwise LEV circulation for each A. Both positive and negative axial flow are found in the first LEV for A = 2 and 4, with the positive component being somewhat larger. This yields a generally positive (outboard) average vorticity flux. The average lift coefficient is essentially constant with A from 1 to 4 during the slow growth phase, although the large-time behaviour shows a slight decrease in lift coefficient with increasing A. The S-DPIV data are used to obtain the lift impulse and the spanwise and streamwise components contributing to the lift coefficient. The spanwise contribution is similar for A = 2 and 4, due to similar trailing-edge vortex interactions, LEV saturation behaviour and total circulation slopes. However, for A = 2 the streamwise contribution is much larger, because of the stronger, coherent TV and aft-tilted LEV, which will create a relatively lower-pressure region over the tip.

High-incidence lift generation via flow reattachment is studied. Different reattachment mechanisms are distinguished, with dynamic manoeuvres and tip vortex downwash being separate mechanisms. We focus on the latter mechanism, which is strictly available to finite wings, and isolate it by considering steadily translating wings. The tip vortex downwash provides a smoother merging of the flow at the trailing edge, thus assisting in establishing a Kutta condition there. This decreases the strength/amount of vorticity shed from the trailing edge, and in turn maintains an effective bound circulation resulting in continued lift generation at high angles of attack. Just below the static lift-stall angle of attack, strong vorticity is shed at the trailing edge indicating an increasingly intermittent reattachment/detachment of the instantaneous flow at mid-span. Above this incidence, the trailing-edge shear layer increases in strength/size representing a negative contribution to the lift and leads to stall. Lastly, we show that the mean-flow topology is equivalent to a vortex pair regardless of the particular physical flow configuration.

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The classical problem of roll-up of a two-dimensional free inviscid vortex sheet is reconsidered. The singular governing equation brings with it considerable difficulty in terms of actual calculation of the sheet dynamics. Here, the sheet is discretized into segments that maintain it as a continuous object with curvature. A model for the self-induced velocity of a finite segment is derived based on the physical consideration that the velocity remain bounded. This allows direct integration through the singularity of the Birkhoff–Rott equation. The self-induced velocity of the segments represents the explicit inclusion of stretching of the sheet and thus vorticity transport. The method is applied to two benchmark cases. The first is a finite vortex sheet with an elliptical circulation distribution. It is found that the self-induced velocity is most relevant in regions where the curvature and the sheet strength or its gradient are large. The second is the Kelvin–Helmholtz instability of an infinite vortex sheet. The critical time at which the sheet forms a singularity in curvature is accurately predicted. As observed by others, the vortex sheet strength forms a finite-valued cusp at this time. Here, it is shown that the cusp value rapidly increases after the critical time and is the impetus that initiates the roll-up process.