A pair of swimming fish: energetics and stability
Résumé
The physical basis for fish schooling is examined using the minimal subsystem of a fish school, consisting in two fish swimming together, using a three-dimensional computational approach. Kinematics and geometry are obtained from previous experimental work [1]. Energy expenditure and efficiency are evaluated using a cost of transport function, while the effect of schooling on the stability of each swimmer is examined by probing the lateral force and the lateral and longitudinal force fluctuations. We construct full maps of the aforementioned quantities as functions of the spatial pattern of the swimming fish pair and show that both energy expenditure and stability can be invoked as possible reasons for the swimming patterns and tail-beat synchronization observed in real fish. Our results suggest that high cost of transport zones should be avoided by the fish. Wake capture may be energetically unfavorable in the absence of kinematic adjustment. We hereby hypothesize that fish may restrain from wake capturing and, instead, adopt side-to-side configuration as a conservative strategy, when the conditions of wake energy harvesting are not satisfied. To maintain a stable school configuration, compromise between propulsive efficiency and stability, as well as between school members, ought to be considered.
[1] I. Ashraf, R. Godoy-Diana, J. Halloy, B. Collignon, B. Thiria. Synchronization and collective swimming pat- terns in fish (Hemigrammus bleheri). Journal of The Royal Society Interface, 13 (123), 20160734 (2016).
[2] G. Li, D. Kolomenskiy, H. Liu, B. Thiria, R. Godoy-Diana On the energetics and stability of a minimal fish school. PLoS ONE 14(8): e0215265 (2019)