A frequency lock-in mechanism in the interaction between wind and crop canopies

The interaction between wind dynamics and the waving of crop canopies is explored. On-site experiments with wheat and alfalfa fields have allowed us to quantify the motion of a large set of plants subject to wind, using an image-correlation technique. The coherent part of the waving motion is extracted by a bi-orthogonal decomposition of the spatio-temporal velocity field of the crop surface. It is shown that the corresponding space and time features cannot be explained using predictions from the mixing-layer analogy of wind above canopies, which is the most common model for perturbations in this environment. We show that the plant bending stiffness plays an important role in the frequency and wavelength selection for the coherent motion of the canopy. A fully coupled model, where the wind fluctuations and the plant dynamics interact through a drag term, is then proposed. This model allows us to demonstrate a lock-in mechanism, similar in principle to what is found in vortex-induced vibration, whereby the frequency of the instability deviates from its expected value when approaching the natural frequency of the oscillating medium. This finding is then compared with data from on-site experiments, and good agreement, in both the frequency and wavelength of the propagating patterns observed on the canopy surface, is found.