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

TL;DR

This study applies a hydrodynamics framework to analyze the motion of a dense sheep flock, revealing edge fluctuations and long-range correlations that are crucial for modeling collective animal behavior.

Contribution

It introduces a hydrodynamics approach to study dense sheep flocks, emphasizing edge dynamics and long-range correlations, which are novel insights in collective animal motion analysis.

Findings

Edge fluctuations propagate like waves.

Large-scale correlations span the entire flock.

Flock remains overall stationary despite internal dynamics.

Abstract

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.