ArticlePublisher preview available

A separated vortex ring underlies the flight of the dandelion

October 2018
Nature 562(7727)

DOI:10.1038/s41586-018-0604-2

Authors:

Madeleine Seale

University of Oxford

Alice Macente

University of Strathclyde

Daniele Certini

The University of Edinburgh

Show all 7 authorsHide

Wind-dispersed plants have evolved ingenious ways to lift their seeds1,2. The common dandelion uses a bundle of drag-enhancing bristles (the pappus) that helps to keep their seeds aloft. This passive flight mechanism is highly effective, enabling seed dispersal over formidable distances3,4; however, the physics underpinning pappus-mediated flight remains unresolved. Here we visualized the flow around dandelion seeds, uncovering an extraordinary type of vortex. This vortex is a ring of recirculating fluid, which is detached owing to the flow passing through the pappus. We hypothesized that the circular disk-like geometry and the porosity of the pappus are the key design features that enable the formation of the separated vortex ring. The porosity gradient was surveyed using microfabricated disks, and a disk with a similar porosity was found to be able to recapitulate the flow behaviour of the pappus. The porosity of the dandelion pappus appears to be tuned precisely to stabilize the vortex, while maximizing aerodynamic loading and minimizing material requirements. The discovery of the separated vortex ring provides evidence of the existence of a new class of fluid behaviour around fluid-immersed bodies that may underlie locomotion, weight reduction and particle retention in biological and manmade structures.

SVR visualization of the wake of 10 fixed dandelion seeds The flow speed is half of the terminal velocity of the seed. Each image was obtained using long-exposure photography.

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SVR visualization of the wake of 10 freely flying dandelion seeds a–j, Each image corresponds to a snapshot from a video of the flight of the dandelions in the wind tunnel. The images show the seeds as they pass through the laser sheet, and the SVR may be difficult to identify in some panels because of the orientation of the laser sheet with respect to the axis of the SVR.

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The breakdown in symmetry in the SVR of dandelion seeds a, b, At low speeds, the SVR is axisymmetric. a, Contrast-enhanced image. b, Original image. c, d, At higher speeds, this symmetry is lost. c, Contrast-enhanced image. d, Original image. a–d, Experiments were repeated independently on n = 10 biological samples, with similar results. e, f, The axisymmetry of SVR at low Re (e) breaks down at higher Re (f).

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Images of porous disks showing the resolution of the technique for disks of various porosities a, b, Impervious disk. c–f, A disk with 33% porosity. g, h, A disk with 55% porosity. i, j, A disk with 75% porosity. k–p, A disk with 89% porosity.

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Steady and unsteady wake behind porous disks and pappi Video snapshots are shown. a–d, The flow visualization behind a solid disk, with a steady wake (a) and an unsteady wake at three time points within one period of vortex shedding (b–d). e–h, The flow around a porous disk (ε = 0.75) with a steady wake (e) and an unsteady wake at three time points within one period of vortex shedding (f–h). i–l, The wake behind a dandelion sample with a steady SVR (i) and at three time points within one period of vortex shedding (j–l).

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LETTER https://doi.org/10.1038/s41586-018-0604-2

A separated vortex ring underlies the flight of the

dandelion

Cathal Cummins1,2,3, Madeleine Seale2,3,4, Alice Macente2,4,5, Daniele Certini1, Enrico Mastropaolo4, Ignazio Maria Viola1* &

Naomi Nakayama2,3,6*

Wind-dispersed plants have evolved ingenious ways to lift their

seeds1,2. The common dandelion uses a bundle of drag-enhancing

bristles (the pappus) that helps to keep their seeds aloft. This passive

flight mechanism is highly effective, enabling seed dispersal over

formidable distances

3,4

; however, the physics underpinning pappus-

mediated flight remains unresolved. Here we visualized the flow

around dandelion seeds, uncovering an extraordinary type of vortex.

This vortex is a ring of recirculating fluid, which is detached owing

to the flow passing through the pappus. We hypothesized that the

circular disk-like geometry and the porosity of the pappus are the

key design features that enable the formation of the separated vortex

ring. The porosity gradient was surveyed using microfabricated

disks, and a disk with a similar porosity was found to be able to

recapitulate the flow behaviour of the pappus. The porosity of the

dandelion pappus appears to be tuned precisely to stabilize the

vortex, while maximizing aerodynamic loading and minimizing

material requirements. The discovery of the separated vortex ring

provides evidence of the existence of a new class of fluid behaviour

around fluid-immersed bodies that may underlie locomotion,

weight reduction and particle retention in biological and manmade

structures.

Dandelions (Taraxacum officinale agg.) are highly successful per

ennial herbsthat can be found in temperate zones all over the world5.

Dandelions, as with many other members of the Asteraceae family,

disperse their bristly seeds using the wind and convective updrafts

6,7

Most dandelion seeds probably land within 2m8,9; however, in warmer,

drier and windier conditions, some may fly further (up to 20,000 seeds

per hectare travelling more than 1km by one estimate)6,10. Asteraceae

seeds routinely disperse over 30km and occasionally even 150km3,4.

Plumed seeds comprise a major class of dispersal strategies used by

numerous and diverse groups of flowering plants, of which the com-

mon dandelion is a representative example. Plumed seeds contain a

bundle of bristly filaments, called a pappus, which are presumed to

function in drag enhancement (Fig.1a–c). The pappus prolongs the

descent of the seed, so that it may be carried further by horizontal

winds11, and may also serve to orientate the seed as it falls7,12.

Dandelion seeds fall stably at a constant speed in quiescent condi-

tions2,13–15. For wind-dispersed seeds, maintaining stability while maxi-

mizing descent time in turbulent winds may be useful for long-distance

dispersal

16,17

. It is not clear, however, why plumed seeds have opted for

a bristly pappus rather than a wing-like membrane, which is known

to enhance lift in some other species (for example, maples1). Here we

analyse the flight mechanism of the dandelion by characterizing the

fluid dynamics of the pappus and identifying the key structural features

enabling its stable flight.

To examine the flow behaviour around the pappus, we built a

vertical wind tunnel (Fig.1d and Methods), which was designed so

that the seed can hover at a fixed height. The flow past the pappus was

visualized for both freely flying (Supplementary Video1) and fixed

(Fig.1e, f and Supplementary Videos2, 3) samples, using long-exposure

photography and high-speed imaging. We found a stable air bubble

(a vortex ring) that is detached from the body, yet steadily remains

a fixed distance downstream of the pappus (Fig.1e, f and Extended

Data Figs.1a–j, 2a–j, 3a–d). Bluff bodies (such as circular disks) may

generate vortex rings in their wake, but these are either attached to the

body or shed from it and advected downstream. The vortex ring in

the wake of the pappus is neither attached nor advected downstream,

and we therefore called this vortex a separated vortex ring (SVR). The

topology of SVRs has been considered theoretically, but was thought

to be too unstable to actually occur18; here we show that the design of

the pappus stabilizes the SVR.

Attached vortex rings form behind circular obstacles; however, it is

unclear how the pappus can generate a vortex ring with such a limited

air–structure interface (that is, high porosity). The morphology of

the dandelion seeds was determined using X-ray computed micro-

tomography (μCT) and light microscopy (Fig.1a–c and Methods). The

pappus was found to comprise n = 100 filaments (95–106 (mean (95%

confidence interval)); n = 10 seeds) that radiate out from a central point

(the pulvinus), each with a mean length (L) of 7.4mm (7.35–7.46mm

(95% confidence interval); n = 937 filaments; Fig.1a, b) and mean diam-

eter (d) of 16.3μm (15.7–17.0 μm (95% confidence interval); n = 10

filaments; Fig.1c). The porosity (ε, defined as the ratio of the empty

projected area to the plan area of the enclosing disk) of the pappus

was measured using light microscopy (Methods) and was found to be

0.916 (0.907–0.923 (mean (95% confidence interval); n = 10 s eeds).

The Reynolds number is a non-dimensional parameter characterizing

the relative importance of inertial to viscous forces in a fluid. The

flow through and around the pappus involves two different Reynolds

numbers: that of the entire pappus (Re = UD/ν, in which U is the velocity

of the seed, D is the diameter of the pappus and ν the kinematic viscosity

of the fluid) and that of an individual filament (Ref = Ud/ν). Our

modelling revealed that the pappus of a dandelion benefits from

a ‘wall effect’19,20 at low Ref (Methods). Neighbouring filaments

interact strongly with one another because of the thick boundary

layer around each filament, which causes a considerable reduction

in air flow through the pappus (Methods). This effect—which was

previously considered to be unimportant for dandelion seeds2,21—

confers the high drag coefficient of the seed, which helps the seed to

remain aloft.

The drag coefficient (C

=F/0.5ρU

A, in which F is the drag force

acting on the seed, ρ is the density of air and A is the projected area of

the pappus) of the dandelion seeds was calculated by measuring the

terminal velocity U = 39.1cms−1 (34.9–43cms−1; mean (95% confi-

dence interval); n = 10 seeds) in a drop test (Fig.2a). The seeds were

ballasted and cut to vary the weight to explore a wide range of Re

(Methods). The mean diameter of the dandelion pappi in our drop tests

was D = 13.8mm (13.2–14.3mm (95% confidence interval); n = 10

seeds). With a mean porosity of ε = 0.916, the total projected area of

1School of Engineering, Institute for Energy Systems, University of Edinburgh, Edinburgh, UK. 2School of Biological Sciences, Institute of Molecular Plant Sciences, University of Edinburgh,

Edinburgh, UK. 3SynthSys Centre for Systems and Synthetic Biology, University of Edinburgh, Edinburgh, UK. 4School of Engineering, Institute for Integrated Micro and Nano Systems, University

of Edinburgh, Edinburgh, UK. 5School of Geographical and Earth Sciences, University of Glasgow, Glasgow, UK. 6Centre for Science at Extreme Conditions, University of Edinburgh, Edinburgh, UK.

*e-mail: i.m.viola@ed.ac.uk; naomi.nakayama@ed.ac.uk

414 | NATURE | VOL 562 | 18 OCTOBER 2018

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