We demonstrate that data from direct numerical simulation of turbulent boundary layers at Mach 3 exhibit the same large-scale coherent structures that are found in supersonic and subsonic experiments, namely elongated, low-speed features in the logarithmic region and hairpin vortex packets. Contour plots of the streamwise mass flux show very long low-momentum structures in the logarithmic layer. These low-momentum features carry about one-third of the turbulent kinetic energy. Using Taylor's hypothesis, we find that these structures prevail and meander for very long streamwise distances. Structure lengths on the order of 100 boundary layer thicknesses are observed. Length scales obtained from correlations of the streamwise mass flux severely underpredict the extent of these structures, most likely because of their significant meandering in the spanwise direction. A hairpin-packet-finding algorithm is employed to determine the average packet properties, and we find that the Mach 3 packets are similar to those observed at subsonic conditions. A connection between the wall shear stress and hairpin packets is observed. Visualization of the instantaneous turbulence structure shows that groups of hairpin packets are frequently located above the long low-momentum structures. This finding is consistent with the very large-scale motion model of Kim & Adrian (1999).

We investigate experimentally the force generated by the unsteady vortex formation of low-aspect-ratio normal flat plates with one end free. The objective of this study is to determine the role of the free end, or tip, vortex. Understanding this simple case provides insight into flapping-wing propulsion, which involves the unsteady motion of low-aspect-ratio appendages. As a simple model of a propulsive half-stroke, we consider a rectangular normal flat plate undergoing a translating start-up motion in a towing tank. Digital particle image velocimetry is used to measure multiple perpendicular sections of the flow velocity and vorticity, in order to correlate vortex circulation with the measured plate force. The three-dimensional wake structure is captured using flow visualization. We show that the tip vortex produces a significant maximum in the plate force. Suppressing its formation results in a force minimum. Comparing plates of aspect ratio six and two, the flow is similar in terms of absolute distance from the tip, but evolves faster for aspect ratio two. The plate drag coefficient increases with decreasing aspect ratio. IntroductionWork on the flapping-wing propulsion of insects and birds has increased greatly in recent years, motivated by its potential application to the design of micro air vehicles. However, there is a corresponding lack of fundamental research on unsteady threedimensional vortex flows at the appropriate low to moderate Reynolds numbers. The present study focuses on understanding the effect of the wingtip vortex on the overall wing force of a hovering insect. This tip effect is dependent on the wing aspect ratio (AR).Flying insects have wing ARs between 2.75 and 6 (Ellington 1984; Dickinson, Lehmann & Sane 1999), while hummingbird wings have ARs of about 4 (Dhawan 1988). Aspect ratio is defined here as b 2 /S, where b is the span of a single wing and S is the single-wing planform (top-view) area. Hovering wing kinematics typically include a segment of downward, plunging motion which tilts the drag force upward so that it contributes to supporting the insect's weight; for dragonflies and hoverflies, drag is the primary wing force keeping the insect aloft (Wang 2004). Here, we focus on drag-based hovering. † Present address:

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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.

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