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arXiv · 2011.01802

Collective orientation of an immobile fish school, effect on rheotaxis

Renaud Larrieu·Catherine Quilliet·Aurélie Dupont·Philippe Peyla
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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.

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Renaud Larrieu, Catherine Quilliet, Aurélie Dupont, Philippe Peyla. 2020-11-03. Collective orientation of an immobile fish school, effect on rheotaxis. https://doi.org/10.1103/physreve.103.022137

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