On the energetics and stability of a minimal fish school

Abstract

The physical basis for fish schooling is examined using three-dimensional numerical simulations of a pair of swimming fish, with kinematics and geometry obtained from experimental data. 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. 2 result from complex social reasons [1-4]. Depending on the species, animals aggregate 3 and modulate group cohesion to improve foraging and reproductive success, avoid 4 predators or facilitate predation. Global cohesive decision and action for the whole 5 group result from different types of interaction at the local scale. Fish schools, for 6 instance, are an archetypal example of how local interactions lead to complex global 7 decisions and motions [5]. Fish interact through vision but also by sensing the 8 surrounding flow using their lateral line system [6]. From the fluid dynamics perspective, 9 hydrodynamic interactions between neighbors have often been associated with swimming 10 efficiency strategies, considering how each individual in the school is affected by the 11 vortical flows produced by its neighbors. Breder [7] already recognized the importance 12 of this issue, and more recent works have described how fish make use of vortices when 13 swimming through an unsteady flow, whether produced by neighboring fish or by other 14 March 27, 2019 1/14 features in the environment (see e.g. the review by Liao [8]). Concerning collaborative 15interactions between swimming fish, the first clear picture was proposed in the early 16 70's by Weihs' pioneering work [9]. He focused on interactions within a two-dimensional 17 layer of a three-dimensional school, and proposed an idealized two-dimensional model in 18 which each individual in the fish school places itself to benefit from the wakes generated 19 by its two nearest neighbors, giving rise to a precise diamond-like pattern. 20Weihs' theory has been followed by extensive experimental verification generally 21 comforting the idea of decreased energetic cost of locomotion in fish schools. Thus, 50We are only aware of two previous three-di...

Burst-and-coast swimmers optimize gait by adapting unique intrinsic cycle

“…i.e., as the power P normalized by the average swimming speed U and the mass of the fish (see ref. 13 and "Methods" for details). The shaded area in each subplot of Fig.…”

Self-directed propulsion of an unconstrained flapping swimmer at low Reynolds number: hydrodynamic behaviour and scaling laws

“…2009; Li et al. 2019). However, it should be pointed out that the fixed foil model has several restrictions for the study of flapping-based propulsion.…”

“…Furthermore, there are other different scaling laws for the performance of a fixed flapping foil (Lau & Kelso 2016;. Based on the studies with fixed flapping foils, several fundamental understandings on flapping-based propulsion have been observed, for both single propulsion and schooling performance of flying/swimming animals in Nature (Godoy-Diana et al 2009;Li et al 2019). However, it should be pointed out that the fixed foil model has several restrictions for the study of flapping-based propulsion.…”

On the interference of vorticity and pressure fields of a minimal fish school

“…By using lateral line, fish may detect the existence, relative position and phase shift between each other, and the sensed information may help fish to coordinate their schooling behavior. The present results can be taken as a reference of our future study on fish schooling hydrodynamics and energetics [16], as well as a reference for the design of artificial swimming devices and planning their collective operation strategy.…”