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A separated vortex ring underlies the flight of the dandelion

Abstract

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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Fig. 1: The dandelion seed and the vortex that it generates.
Fig. 2: The forces on dandelion seeds compared with those on solid disks.
Fig. 3: Flow diagnostics of the SVR for the dandelion seeds and a circular disk with comparable porosity.
Fig. 4: The loss of stability of the wakes past porous disks and dandelion seeds.

Data availability

The datasets generated and/or analysed during the current study are available from the corresponding author upon reasonable request.

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Acknowledgements

This work was supported by the Leverhulme Trust (RPG-2015-255) and the Royal Society (UF140640). We thank I. Butler (Geosciences, University of Edinburgh) for assistance with the μCT scans; and A. Firth and M. Mason (Engineering, University of Edinburgh) for helping to build the wind tunnel.

Reviewer information

Nature thanks M. Dickinson and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Author information

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Authors

Contributions

C.C., E.M., I.M.V. and N.N. designed the experiments. C.C. designed and set up the wind tunnel. C.C. carried out the numerical analyses, the flight assay and flow visualization with assistance from M.S. and D.C. C.C. designed and E.M. fabricated the silicon disks. A.M. optimized and performed the μCT scans, and M.S. analysed the resulting 3D images. C.C. wrote the manuscript; M.S., E.M., I.M.V. and N.N. helped with revision and editing. E.M., I.M.V. and N.N. designed and oversaw the project; I.M.V. supervised the investigations of fluid mechanics and N.N. supervised the biological and structural studies.

Corresponding authors

Correspondence to Ignazio Maria Viola or Naomi Nakayama.

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The authors declare no competing interests.

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Extended data figures and tables

Extended Data Fig. 1 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.

Extended Data Fig. 2 SVR visualization of the wake of 10 freely flying dandelion seeds.

aj, 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.

Extended Data Fig. 3 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. ad, 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).

Extended Data Fig. 4 Images of porous disks showing the resolution of the technique for disks of various porosities.

a, b, Impervious disk. cf, A disk with 33% porosity. g, h, A disk with 55% porosity. i, j, A disk with 75% porosity. kp, A disk with 89% porosity.

Extended Data Fig. 5 Steady and unsteady wake behind porous disks and pappi.

Video snapshots are shown. ad, 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 (bd). eh, 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 (fh). il, The wake behind a dandelion sample with a steady SVR (i) and at three time points within one period of vortex shedding (jl).

Extended Data Fig. 6 The experimental setup for laser Doppler anemometry and flow visualization.

a, b, Schematic drawings of the experimental setup for laser Doppler anemometry to measure the flow speed and turbulent intensity in the wind tunnel (a) and the experimental setup for flow visualization in the wind tunnel using a CW laser and high-speed camera (b). c, Photograph of the actual experimental setup for flow visualization.

Extended Data Fig. 7 Workflow for post-processing of the μCT scan data.

Image processing workflow for analysis of µCT data indicating the algorithms performed and the software used (Avizo or R).

Extended Data Fig. 8 The flow past a porous disk using direct numerical simulations and boundary integral methods.

ac, The axial velocity uz/U (a), pressure p/ρU2 (b) and streamlines (c), showing the presence of an SVR with upstream and downstream stagnation points zsu and zsd, respectively. d, The reduction in the drag force on filaments within an array moving at slow speeds calculated using a boundary integral method. The force Di on the ith filament of a rectangular pappus, divided by the drag force for an isolated filament D0.

Extended Data Table 1 μCT scan-acquisition settings
Extended Data Table 2 Morphological data of dandelion seeds

Supplementary information

Supplementary Information

This file contains Supplementary Discussions of the experiments (fixed and freely flying dandelions and porous disks) and further details of the microfabricated structures.

Reporting Summary

Supplementary Data

This file contains source data for the graphs in Figures 2-4, Extended Data Figure 8 and Extended Data Table 2.

Video 1

: SVR visualization in the wake of a freely flying dandelion seed. In this video, the dandelion seed is allowed to fly freely in the wind tunnel, and the SVR is visualized as the dandelion passes through the laser sheet. These experiments were repeated independently for n = 10 biological replicates with similar results.

Video 2

: SVR visualization in the wake of a fixed dandelion seed (low speed). In this video, the SVR is visualized by keeping the seed fixed in a low speed air flow. These experiments were repeated independently for n = 10 biological replicates with similar results.

Video 3

: SVR visualization in the wake of a fixed dandelion seed (high speed). In this video, the SVR is visualized by keeping the seed fixed in the air flow at terminal velocity. These experiments were repeated independently for n = 10 biological replicates with similar results.

Video 4

: SVR visualization in the wake of fixed disks of varying porosities. In this video, there are four panels. The bottom panels are visualizations of the flow past an impervious disk in steady (left) and unsteady (right) conditions. The top panels are visualizations of the flow past a porous disk (75% porous) in steady (left) and unsteady (right) conditions. Similar experiments were performed 15 times (each experiment had a different Reynolds number) for each disk with similar results.

Video 5

: SVR visualization in the wake of fixed disks of varying porosities (high porosity). In this video, there are four panels. The bottom panels are visualizations of the flow past a porous disk (89% porous) in steady (left) and unsteady (right) conditions. The top panels are visualizations of the flow past a porous disk (92% porous) in steady (left) and unsteady (right) conditions. Similar experiments were performed 20 and 17 times (each experiment had a different Reynolds number) for the 89% and 92% porous disks respectively with similar results.

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Cummins, C., Seale, M., Macente, A. et al. A separated vortex ring underlies the flight of the dandelion. Nature 562, 414–418 (2018). https://doi.org/10.1038/s41586-018-0604-2

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Keywords

  • Separate Vortex Ring (SVR)
  • Taraxacum
  • Dandelion Seeds
  • Pappus
  • Kinematic Viscosity Measurements

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