By bending and twisting under fluid loading, plants reduce their projected area per-
pendicular to the flow and also become more streamlined [1]. Through reconfiguration,
the drag load plants must support does not grow with the square of the velocity of the
flow they are subjected to - as it would on a rigid bluff body - but rather more slowly. It
was shown with systems of simple geometries like flexible fibres [2], and disks [3] that the
reconfiguration can be quantified. This allowed to derive values of the Vogel exponent,
which scales the ability to reduce drag, comparable with those found in experiments [4].
Continuing in this direction, we propose an experimental investigation in air on the
drag of flexible plates of simple geometries found in plant systems, combined with a
theoretical modelling of their deformation. These geometries include rectangular plates,
circular plates cut along their diameters, as in Acetabularia or a porous sphere made
of flexible radiating beams. In Fig. 1 the photographs of the typical deformation of a
circular plate specimen at increasing flow velocity are shown. The behaviour of the plate
folding in the flow is well captured by a simple beam model coupled with an empirical
drag formulation, as can be seen on the right part of the figure. Through extensive wind-
tunnel testing, the dimensionless parameters that characterise the problem are found,
following the approach used in [5]. Finally, the relation between the geometry of the
plant or the organ and the abilty to reduce drag by flexibility is discussed.
Figure 1: Left : deformation of a flexible disk under flow. Right : drag coefficient as a
function of the Cauchy number
[1] Vogel, S. 1996 Life in Moving Fluids, 2nd edn. Princeton University Press.
[2] Alben, S., Shelley, M. & Zhang, J. 2002 Nature 420, 479481.
[3] Schouveiler, L. & Boudaoud, A. 2006 J. Fluid Mech. 563, 71-80.
[4] Harder,D., Speck, O., Hurd, C. & Speck, T. 2004. J. Plant Growth Regul., 23,
98107.
[5] de Langre, E. 2008 Annual Review of Fluid Mechanics 40, 141168.
1