Hydrodynamics of Turning Flocks

Xingbo Yang, M. Cristina Marchetti

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


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 wavelengths. This mode becomes unstable as a result of the growth of bend and splay deformations augmented by the spin wave, signaling the transition to complex spatiotemporal patterns of continuously turning and swirling flocks.

Original languageEnglish (US)
Article number258101
JournalPhysical Review Letters
Issue number25
StatePublished - Dec 17 2015

ASJC Scopus subject areas

  • General Physics and Astronomy


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