Hydrodynamics of Turning Flocks

TL;DR

This paper develops a hydrodynamic model of flocking that includes turning inertia, revealing how spin waves and bend elasticity influence turning behavior and pattern formation in flocks.

Contribution

It introduces a generalized hydrodynamic model incorporating turning inertia into flocking dynamics, derived from an inertial spin model, and analyzes the resulting wave modes and instabilities.

Findings

Identification of anisotropic spin waves mediating turning information

Discovery of an angular-dependent hydrodynamic mode with long-wavelength instability

Prediction of transition to complex swirling flock patterns

Abstract

We present a hydrodynamic model of flocking that generalizes the familiar Toner-Tu equations to incorporate turning inertia of well-polarized flocks. The continuum equations controlled by only two dimensionless parameters, orientational inertia and alignment strength, are derived by coarse graining the inertial spin model recently proposed by Cavagna et al. The interplay between orientational inertia and bend elasticity of the flock yields anisotropic spin waves that mediate the propagation of turning information throughout the flock. The coupling between spin current density to the local vorticity field through a nonlinear friction gives rise to a hydrodynamic mode with angular-dependent propagation speed at long wavelength. This mode goes unstable as a result of the growth of bend and splay deformations augmented by the spin wave, signaling the transition to complex spatio-temporal patterns of continuously turning and swirling flocks.