Complexity and self-organization in large arrays of elastic rods in an air cross-flow

摘要

Experiments on spatio-temporal dynamics in large arrays of cantilevered elastic-rods in uniform and stationary wind-tunnel cross-flow have been carried out. From 90 to 1000 steel and polycarbonate rods with gap ratios ranging from 1.0 to 2.5 are used. As the Reynolds number (based on the rod diameter) increases, a pattern with the characteristics of spatiotemporal chaos emerges in the global behavior of the array of elastic rods. There are local and global patterns. The local patterns are composed of transient rest, linear motions and elliptical motions. In the 90-rod experiments, a cluster-pattern entropy measure is introduced based on these three patterns as a quantitative measure of the local complexity. Below a threshold wind velocity, no significant dynamics appears. Video images reveal that at first each rod moves individually, then clusters consisting of several rods emerge and finally global wave-like motion takes place with higher flow velocities. Spatial patterns in the rod-density distribution appear as more rods suffer impacts with nearest neighbors. Furthermore, these collective nonlinear motions of rods are observed and categorized into several global modes. Using accelerometer data, the rod impact rate versus flow velocity shows a power-law scaling relation. This phenomenon may have application to plant-wind dynamics and damage as well as fluid-structure heat exchange systems. This experiment may also be a two dimensional analog of the impact dynamics of granular materials in a flow.