Hydrodynamics of a dense flock of sheep: edge motion and long-range correlations

Sheep are gregarious animals, and they often aggregate into dense, cohesive flocks, especially under stress. In this paper, we use image processing tools to analyze a publicly available aerial video showing a dense sheep flock moving under the stimulus of a shepherding dog. Inspired by the fluidity of the motion, we implement a hydrodynamics approach, extracting velocity fields, and measuring their propagation and correlations in space and time. We find that while the flock overall is stationary, significant dynamics happens at the edges, notably in the form of fluctuations propagating like waves, and large-scale correlations spanning the entire flock. These observations highlight the importance of incorporating interfacial dynamics, for instance in the form of line tension, when using a hydrodynamics framework to model the dynamics of dense, non-polarized swarms.

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