Localized inhomogeneity and position-dependent stability of migratory bird formations

TL;DR

This study models how localized inhomogeneity, like wingspan changes, influences the geometry and stability of migratory bird formations, revealing position-dependent stability effects.

Contribution

It introduces a dynamical framework using a lifting-line model to analyze the impact of localized individual differences on formation stability.

Findings

Stable formations are sensitive to wingspan modifications.

Stability range varies with the position of the modified bird.

Homogeneous formations naturally form a U-shaped geometry.

Abstract

We investigate how localized inhomogeneity affects the geometry and stability of migratory bird formations. We use a lifting-line model with a horseshoe-vortex representation to describe the longitudinal dynamics of aerodynamic interactions. As a reference case, we first analyze homogeneous formations and show that their steady states exhibit a U-shaped geometry with hierarchical streamwise spacing, in which adjacent birds become progressively closer toward the leader. We then introduce localized inhomogeneity by modifying the wingspan of a single bird, with its physical properties determined by scaling relations. We determine the range of wingspan variation that preserves a stable formation. The stability range depends strongly on the position of the modified bird, being narrower near the outer wing and broader near the leader. These findings provide a minimal dynamical framework for understanding how local aerodynamic interactions and localized individual differences affect collective flight structures.