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A separated vortex ring underlies the flight of the dandelion

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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.
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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-
tions2,1315. 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
D
=F/0.5ρU
2
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s1 (34.9–43cms1; 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
© 2018 Springer Nature Limited. All rights reserved.
... Membranes are ubiquitous in the biological world. Some unicellular organisms use thin permeable structures in their displacement and feeding strategies 6 or plants use them to spread their seeds 7,8 . Solvent (water) and solute (sugar) translocation across aquaporin porous channels constellating the cellular membranes is a primary process for the good performance of organisms, spanning from plants 9,10 to animals 11 . ...
... withκ eff =κ|∂M|. Equation (14) can be used together with model (7,8) to calculate a reference value of concen-trationĈ 0 at the macroscopic membrane, which depends on the values of α, β and γ. While in case of Neumann and Robin condition the value ofĈ 0 is not known a priori, for the case of DirichletĈ 0 assumes the constant value ofĈ w on the membrane. ...
... All equations mentioned above are numerically implemented via their weak formulation in the finite element solver COMSOL Multiphysics, using a domain decomposition method 64 to couple the upward and downward solvent flow and solute fluxes. In this framework, macroscopic models (42,40) and (7,8) are interface conditions between two domains, respectively. To exchange information from the upward to the downward domain, the stress jump and concentration flux conditions are implemented by exploiting the interface integral emerging from the weak formulation of the corresponding governing equations, while, to exchange information from the downward to the upward domain, the continuity of velocity and concentration is imposed via a Dirichlet boundary condition. ...
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... Plants cover a large fraction of the Earth's land mass despite most species having limited to no mobility. To transport their propagules, many plants have evolved mechanisms to disperse their seeds using the wind [1][2][3][4] . A dandelion seed, for example, has a bristly filament structure that decreases its terminal velocity and helps orient the seed as it wafts to the ground 5 . ...
... Plants have evolved various mechanisms to use wind for seed dispersal over a wide area [1][2][3][4] including creating lightweight diaspores with plumose or comose structures that act as drag-enhancing parachutes 6,7 . Asteraceae plants, such as the common dandelion, produce plumed seeds containing a pappus, which is a bundle of bristly filaments 1 . ...
... Plants have evolved various mechanisms to use wind for seed dispersal over a wide area [1][2][3][4] including creating lightweight diaspores with plumose or comose structures that act as drag-enhancing parachutes 6,7 . Asteraceae plants, such as the common dandelion, produce plumed seeds containing a pappus, which is a bundle of bristly filaments 1 . The pappus increases the drag experienced by the diaspores, decreasing their terminal velocity. ...
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... Mink was interested in explaining what is happening when ahistorian draws together a range of different influences and causes to produce a historical narrative, to make coherence out of that complexity. As Mink wrote in33 Cummins et al. 2018, p. 414. 34 Norton Wise, 2017 things together' in a total and synoptic judgement which cannot be replaced by any analytic technique". ...
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This chapter introduces philosophers of engineering to a new research agenda currently permeating the history and philosophy of science, one concerned with the functions of narrative in science. The functions of narrative that I am here interested in contribute to two particular kinds of epistemic positioning. First, that of the individual researcher’s epistemic position in relation to a field of inquiry. Second, the positioning of a community of researchers gathered around and looking at newly acquired evidence, assessing its significance. In the first, the kind of inference and hypothesis making that narrative affords stimulates and orders inquiry. In the second, narrative supplies a means of reasoning from the particulars of a case to something deeper or broader. The case analysed concerns an interdisciplinary project between engineers, applied mathematicians, and biologists dedicated to understanding how dandelion seeds fly. My analysis draws on the concepts of ‘tellability’ from literary study and ‘synoptic judgment’ from the philosophy of history. Tellability is used to explore question generation in science and engineering, in particular the making of more or less ‘askable’ questions. Synoptic judgement is used to interrogate my own case, key elements of which resemble synoptic judgement without assimilating to it.
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Chapter
The readers are first made aware of everyday external flows in this chapter. Lift and drag are then introduced, followed by discussion on fluid viscosity and boundary layer. Flow over a flat plate is subsequently presented. The boundary layer development from laminar to transition to turbulent is delineated. Bluff body aerodynamics, including vortex shedding and streamlining, is elucidated. On this, the familiar flow around a circular cylinder is illustrated.
Chapter
This chapter differentiates a fluid from a solid. It explains what a continuum fluid is. Examples of beautiful natural fluids in motions are used to illustrate the importance of moving fluids. Fluid viscosity is timely introduced, where viscosity is not a function of flow shear for Newtonian fluids. The chapter wraps up by providing a general categorization of various fluid motions encountered in nature and in engineering.
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