Paper waves in the wind

TL;DR

This study investigates how flexible sheets subjected to wind develop waves, revealing scaling laws for wave frequency and wavenumber that could inform future energy harvesting technologies.

Contribution

The paper introduces experimental measurements and analytical scaling laws for wind-induced wave selection on flexible sheets, spanning a wide rigidity range.

Findings

Wave frequency and wavenumber follow simple scaling laws.

Scaling laws involve a gravity-induced velocity scale.

Data collapse achieved across two orders of magnitude in rigidity.

Abstract

A flexible sheet clamped at both ends and submitted to a permanent wind is unstable and propagates waves. Here, we experimentally study the selection of frequency and wavenumber as a function of the wind velocity. These quantities obey simple scaling laws, which are analytically derived from a linear stability analysis of the problem, and which also involve a gravity-induced velocity scale. This approach allows us to collapse data obtained with sheets whose flexible rigidity is varied by two orders of magnitude. This principle may be applied in the future for energy harvesting.