Smart wing rotation and trailing-edge vortices enable high frequency mosquito flight

Abstract

Mosquitoes exhibit unusual wing kinematics; their long, slender wings flap at remarkably high frequencies for their size (>800 Hz)and with lower stroke amplitudes than any other insect group. This shifts weight support away from the translation-dominated, aerodynamic mechanisms used by most insects, as well as by helicopters and aeroplanes, towards poorly understood rotational mechanisms that occur when pitching at the end of each half-stroke. Here we report free-flight mosquito wing kinematics, solve the full Navier-Stokes equations using computational fluid dynamics with overset grids, and validate our results with in vivo flow measurements. We show that, although mosquitoes use familiar separated flow patterns, much of the aerodynamic force that supports their weight is generated in a manner unlike any previously described for a flying animal. There are three key features: leading-edge vortices (a well-known mechanism that appears to be almost ubiquitous in insect flight), trailing-edge vortices caused by a form of wake capture at stroke reversal, and rotational drag. The two new elements are largely independent of the wing velocity, instead relying on rapid changes in the pitch angle (wing rotation) at the end of each half-stroke, and they are therefore relatively immune to the shallow flapping amplitude. Moreover, these mechanisms are particularly well suited to high aspect ratio mosquito wings.

Extended Data Figure 1

Mosquito kinematics acquisition rig, wing lengths and mean kinematic patterns. a, CAD representation and b, photograph of the apparatus used to record the body motion and wing kinematics of mosquitoes. The recording volume lies at the intersection of the fields of view of eight high-speed cameras, each creating a silhouette image of the mosquito by the shadow from high power IR-LED illumination. c, wing length estimates for mosquitoes captured in each of 15 sequences (M01-M15). Each estimate shows the median as a black line with shading representing the 95% confidence interval based upon all wing beats from each sequence. Green and purple boxes group sequences that could not be reliably separated using Tukey’s Honestly Significant Difference criterion, although they may come from different individuals of very similar size. As such, our fully-processed dataset of 15 sequences comprises between 12 and 15 individual mosquitoes. d, mean wing beat kinematics for all wingbeats in each of 15 recorded sequences. With reference to c, M01, M06 and M09, coloured green, may be from the same individual. Similarly, M05 and M11 may also be from a single individual.

Extended Data Figure 2

Wing surface pressure distribution and fluid flow visualised by streamlines showing consistency across each of the 15 mosquito sequences. Each image corresponds to key instant t1. Formation of the trailing-edge vortex due to capture of the induced flow from the preceding upstroke causes a distinct region of low pressure on the posterior portion of the wing.

Extended Data Figure 3

Wing surface pressure distribution and fluid flow visualised by streamlines showing consistency across each of the 15 mosquito sequences. Each image corresponds to key instant t2. The downstroke force peak is dominated by a leading-edge vortex and corresponding low pressure on the anterior portion of the wing. The trailing-edge vortex has usually shed by this point in the stroke cycle.

Extended Data Figure 4

Wing surface pressure distribution and fluid flow visualised by streamlines showing consistency across each of the 15 mosquito sequences. Each image corresponds to key instant t3. A low pressure region is evident on the posterior portion of the wing due to lift from rotational drag as the wing rotates around an axis close to the leading edge.

Extended Data Figure 5

Wing surface pressure distribution and fluid flow visualised by streamlines showing consistency across each of the 15 mosquito sequences. Each image corresponds to key instant t4. Formation of a trailing-edge vortex on the aerodynamic upper, (anatomical ventral) surface of the wing during the upstroke due to capture of the induced flow from the preceding downstroke causes a distinct region of low pressure on the posterior portion of the wing.

Extended Data Figure 6

Wing surface pressure distribution and fluid flow visualised by streamlines showing consistency across each of the 15 mosquito sequences. Each image corresponds to key instant t5. A low pressure region exists over much of the aerodynamic upper, (anatomical ventral) surface of the wing as the result of a combination of rotational drag (caused by wing rotation around an axis close to the leading edge) and the remnants of the upstroke’s leading-edge vortex (which is no longer coherent in most examples but is retained in M03, M04, M06, M08, M11).

Extended Data Figure 7

Comparison of the local flow conditions at the trailing edge of the wings of mosquitoes and fruit flies during pronation (t/T=0.09). The comparatively higher local angle of attack at the mosquito is caused by the induced flow from the preceding upstroke. This is a product of kinematic tuning and a form of wake capture that leads to roll up of a transient, coherent, trailing-edge vortex. The vortex contributes to weight support along much of the length of the slender mosquito wing, despite it having little ground velocity during the rotational phase of the stroke cycle.

Extended Data Figure 8

Comparison of computed CFD lift force (black) compared against a simple quasi-steady model (grey) for each of 15 mosquito flight sequences. Orange shading shows where the quasi-steady model over-predicts the force estimate from the CFD simulation, whereas green shows under-prediction. (See also Fig. 3)

Extended Data Figure 9

Lift and drag polars from high-fidelity CFD simulations of the mosquito wing model in continuous rotational sweep at four Reynolds numbers. These were used to create dynamic lift coefficients for the blade element modelling with quasi-steady assumption. Coefficients are calculated for the third rotation, to account for the reduction in effective angle of attack when wings operate in the induced downwash from the preceding wing stroke.

Extended Data Figure 10

Morphology extraction (a, c) and the CFD grid used for simulations (b, d-f). We used the mean wing planform of three mosquitoes, extracted from microscope images of recently excised wings, to generate the wing grids used in our CFD simulations. The body shape was approximated from the silhouettes in the raw video data by fitting ellipses normal to the central axis of the body taken from each of the eight camera views. g, CFD grid and time-step independence was verified after performing simulations with variable cell density and time-step intervals.

Figure 1

Low-amplitude mosquito kinematics. a, three axes and angles that define flapping wing kinematics; stroke position, φ (within the stroke plane, pink), wing pitch angle, α, deviation angle, θ. b, eight views of a C. quinquefasciatus mosquito, showing automated extraction of wing outlines. c, standardized stroke cycle kinematics from one individual (mean±s.d.; n=33 wingbeats). Pitch angle, α, is shown for the base and tip of the wing to highlight longitudinal twist and pitching rotations that are important for unsteady aerodynamics. d, dorsal (top) and lateral (bottom) views of characteristic motions (R=0.75 wing length) for, left-to-right, mosquito, fruit fly, honeybee and hawkmoth. Reynolds numbers (based on mean tip velocity and mean chord length) and aspect ratios for each insect are given,,.

Figure 2

Validation of CFD (a) with PIV (b) quantitative flow fields. Left-to-right: End of pronation (t/T = 0.22), late downstroke (t/T = 0.36), end of supination (t/T = 0.70) and late upstroke (t/T = 0.84); green shading shows areas of no data. Red and blue patches show clockwise and anticlockwise vorticity. Flow velocity field planes are shown at R = 0.5 wing length for both CFD and PIV.

Figure 3

Aerodynamic forces generated by the wings and the mechanisms that produce them: trailing-edge vortices, leading-edge vortices and rotational drag. a, single-wing total aerodynamic force (red), lift (black), drag (blue) and side-force (green). b, lift from CFD (black) compared against a simple quasi-steady model (grey). Orange shading shows where the quasi-steady model over-predicts the force estimate from the CFD simulation, whereas green shows under-prediction. c, partitioning of the lift force (black) into the portion derived from the integrated pressure on the anterior half of the wing (purple), the posterior half (cyan), and the viscous contribution (dashed). Note the fluctuating contributions during the downstroke (t/T = 0-0.5). d, aerodynamic power. e, the effect of increasing wing stroke amplitude (see insert for range) while maintaining mean wing tip velocity is to reduce the relative contribution to lift attributable to unsteady effects. f-j, surface pressure at t1-t5 on the wing (blue to red shading). Overlain are instantaneous streamlines (grey) and flow velocity vectors (black arrows) for selected vertical slices through the three-dimensional flow field at planes 0.6R or 0.75R from wing base. Body (dashed line) and wing outlines (solid line, leading edge in bold) are shown for orientation.

Figure 4

Wing pronation. a, the end of each half stroke in mosquitoes is characterized by a shift in the rotational axis (green dot) from leading to trailing edge. Black arrows indicate local motion of the wing during pronation (at 0.75R, indicated in top row); red arrows indicate the resultant aerodynamic force vector (depicted at the chord-wise centre of pressure). Despite rapid pitching down at t/T=0.10 and faster motion of the leading edge, the trailing edge remains almost stationary yet generates the majority of the lift at this instant due to the formation of a trailing edge vortex caused by the induced flow from the preceding upstroke. Pressure distributions (shaded blue to red) on the upper surface of the mosquito (b) and fruit fly (c) at five moments through the downstroke. Red arrows in (b) show the signature of the trailing-edge vortex, visualised by a region of intense low pressure along the trailing portion of the wing, which is not present on the fruit fly wing (c). Later in the downstroke, a low pressure region from the leading-edge vortex starts outboard and grows towards the wing root, as described elsewhere for both species (green arrow).