Flow dynamics of a dandelion pappus: A linear stability approach

Abstract

The study and control of flow instabilities is a key problem in aerodynamics. Aircrafts are designed not only to generate the lift force needed to balance their weight but, more importantly, to be stable and reasonably steady when in cruise conditions. Similar flow stability properties are naturally achieved by biological flying objects such as the dandelion seeds that are transported by the wind owing to a disklike structure called a pappus. The pappus creates a parachute flow configuration and is a remarkable prototype of how the wake, which would be unsteady if the pappus was completely impermeable, can be stabilized by changing the body structure so as to allow the flow to pass through. We approach the problem using the approximation of an anisotropic and nonhomogeneous rigid porous disk, combined with the linear stability analysis technique. The results show the presence of a mean porosity threshold beyond which the flow is always characterized by a separated, steady, and axisymmetric recirculating vortex ring. We compare our results with those of real dandelion pappi. The threshold is very close to the experimentally observed values of porosity, explaining why the morphology of the pappus promotes a steady wake regime.

Homogenization-based design of microstructured membranes: wake flows past permeable shells

“…The analysis of the stability properties of the steady wake shows the strong stabilization effect of the filtrability number. The marginal stability curves strongly resemble those outlined in Ledda et al (2018Ledda et al ( , 2019. In particular, the vortex shedding is suppressed for large enough values of the filtrability.…”

“…Dandelion seeds are transported in the air by a structure called pappus, which behaves as a parachute. The presence of voids markedly decreases the falling velocity and stabilizes the steady flow (Cummins et al 2018;Ledda et al 2019). At smaller scales, thin permeable shells are of essential importance for unicellular organisms as a key point in their displacement and feeding strategies (Asadzadeh et al 2019).…”

Environmental morphing enables informed dispersal of the dandelion diaspore

“…For dry diaspores A separated vortex ring (SVR) forms behind the pappus due to the high porosity of the pappus combined with precise spacing of the hairs, which limits air flow through the pappus. (Cummins et al, 2018;Ledda et al, 2019). The nature of the SVR behind circular disks is strongly affected by the porosity of the disk and its projected area.…”

Sepal Identity of the Pappus and Floral Organ Development in the Common Dandelion (Taraxacum officinale; Asteraceae)

“…We investigated the development of the pappus in dandelion in detail, aiming to develop the use of dispersal capacity for urban evolution studies in plants. The pappus plays an important role in the dispersal of the seeds and fruits of the Asteraceae [ 1 , 2 ], and variation in the pappus may directly lead to differences in dispersal ability [ 3 , 4 ] allowing plants to anticipate changing environments. To measure such changes and determine how quickly they occur in response to changing environments, we should first characterize pappus development and investigate pappus–sepal homology.…”

“…The pappus is placed on a shorter or longer stalk named a beak (also rostrum ; up to ~1 cm long) and opens into a parachute or disk-like structure at maturity. Aerodynamic studies confirmed that the pappus is a highly effective flight mechanism that generates a lift force needed to balance fruit weight and an axis-symmetric, recirculating vortex ring to stabilize when in cruise conditions [ 1 , 4 ]. To allow adequate permeability for the flow to create a separate vortex ring, the number of pappus parts is important and optimal at ~100 parts, equalling the number commonly found in dandelions.…”