The rolling up of sheets in a steady flow

Abstract

The mechanism of reconfiguration of broad leaves subjected to wind loading is investigated. Circular plastic sheets cut along a radius are immersed in a water flow. They roll up into cones when held at their centres. The opening angle of the cone and the drag force exerted on the sheet are measured as a function of the flow velocity and of the sheet bending rigidity. The cone becomes sharper when the velocity increases or when the sheet stiffness decreases; the reconfiguration leads to a decrease in the drag coefficient. Scaling laws are derived from the mechanical equilibrium of the sheets – the balance between form drag and elastic forces – and the experimental data collapse onto master curves. Two models for the pressure field yield theoretical curves in semi-quantitative agreement with the experiments.