Collective movement of schooling fish reduces the costs of locomotion in turbulent conditions.

The ecological and evolutionary benefits of energy-saving in collective behaviors are rooted in the physical principles and physiological mechanisms underpinning animal locomotion. We propose a turbulence sheltering hypothesis that collective movements of fish schools in turbulent flow can reduce the total energetic cost of locomotion by shielding individuals from the perturbation of chaotic turbulent eddies. We test this hypothesis by quantifying energetics and kinematics in schools of giant danio (Devario aequipinnatus) and compared that to solitary individuals swimming under laminar and turbulent conditions over a wide speed range. We discovered that, when swimming at high speeds and high turbulence levels, fish schools reduced their total energy expenditure (TEE, both aerobic and anaerobic energy) by 63% to 79% compared to solitary fish (e.g., 228 versus 48 kj kg-1). Solitary individuals spend approximately 22% more kinematic effort (tail beat amplitude•frequency: 1.7 versus 1.4 BL s-1) to swim in turbulence at higher speeds than in laminar conditions. Fish schools swimming in turbulence reduced their three-dimensional group volume by 41% to 68% (at higher speeds, approximately 103 versus 33 cm3) and did not alter their kinematic effort compared to laminar conditions. This substantial energy saving highlights that schooling behaviors can mitigate turbulent disturbances by sheltering fish (within schools) from the eddies of sufficient kinetic energy that can disrupt locomotor gaits. Therefore, providing a more desirable internal hydrodynamic environment could be one of the ecological drivers underlying collective behaviors in a dense fluid environment.

Reconstructing the pressure field around swimming fish using a physics-informed neural network.

Fish detect predators, flow conditions, environments and each other through pressure signals. Lateral line ablation is often performed to understand the role of pressure sensing. In the present study, we propose a non-invasive method for reconstructing the instantaneous pressure field sensed by a fish's lateral line system from two-dimensional particle image velocimetry (PIV) measurements. The method uses a physics-informed neural network (PINN) to predict an optimized solution for the pressure field near and on the fish's body that satisfies both the Navier-Stokes equations and the constraints put forward by the PIV measurements. The method was validated using a direct numerical simulation of a swimming mackerel, Scomber scombrus, and was applied to experimental data of a turning zebrafish, Danio rerio. The results demonstrate that this method is relatively insensitive to the spatio-temporal resolution of the PIV measurements and accurately reconstructs the pressure on the fish's body.