Collective orientation of an immobile fish school, effect on rheotaxis

TL;DR

This study models the collective orientation of an immobile fish school using an Ornstein-Uhlenbeck process, revealing how alignment and rheotaxis influence the school's behavior under noise and flow conditions.

Contribution

It introduces a model for immobile fish school orientation dynamics incorporating inertial effects and rheotaxis, extending previous models for mobile fish schools.

Findings

Orientation decreases with noise but faster reorientation improves order.

In flow, fish tend to align against the stream, maintaining immobility.

Rheotaxis is enhanced by alignment interactions in noisy environments.

Abstract

We study the orientational order of an immobile fish school. Starting from the second Newton's law, we show that the inertial dynamics of orientations is ruled by an Ornstein-Uhlenbeck process. This process describes the dynamics of alignment between neighboring fish in a shoal, a dynamics already used in the literature for mobile fish schools. Firstly, in a fluid at rest, we calculate the global polarization (i.e. the mean orientation of the fish) which decreases rapidly as a function of the noise. We show that the faster a fish is able to reorient itself, the more the school can afford to reorder itself for important noise values. Secondly, in the prescence of a stream, each fish tends to orient itself and swims against the flow: the so-called rheotaxis. So even in the presence of a flow, it results in an immobile fish school. By adding an individual rheotaxis effect to alignment interaction between fish, we show that in a noisy environment, individual rheotaxis is enhanced by alignment interactions between fish.