The fluid dynamics of collective vortex structures of plant-animal worms

TL;DR

This study investigates the fluid dynamics of collective vortex structures formed by the plant-animal worm Symsagittifera roscoffensis, combining experiments and models to understand the flow fields and stability of circular mills.

Contribution

It introduces a fluid dynamical model of worm circular mills, emphasizing singularities like source dipoles and quadrupoles, and explains the emergence and stability of multiple mills.

Findings

A rigid disc model captures experimental flow patterns.

Singularities like source dipoles dominate the flow.

Multiple mill stability is explained by the model.

Abstract

Circular milling, a stunning manifestation of collective motion, is found across the natural world, from fish shoals to army ants. It has been observed recently that the plant-animal worm $Symsagittifera~roscoffensis$ exhibits circular milling behaviour, both in shallow pools at the beach and in Petri dishes in the laboratory. Here we investigate this phenomenon, through experiment and theory, from a fluid dynamical viewpoint, focusing on the effect that an established circular mill has on the surrounding fluid. Unlike systems such as confined bacterial suspensions and collections of molecular motors and filaments that exhibit spontaneous circulatory behaviour, and which are modelled as force dipoles, the front-back symmetry of individual worms precludes a stresslet contribution. Instead, singularities such as source dipoles and Stokes quadrupoles are expected to dominate. A series of models is analyzed to understand the contributions of these singularities to the azimuthal flow fields generated by a mill, in light of the particular boundary conditions that hold for flow in a Petri dish. A model that treats a circular mill as a rigid rotating disc that generates a Stokes flow is shown to capture basic experimental results well, and gives insights into the emergence and stability of multiple mill systems.