Hydrodynamic analysis of fish schools arranged in the vertical plane

Abstract

Schools of fish can provide individuals with hydrodynamic advantages, thereby improving the swimming efficiency. Fish schools in nature are mostly spatial configurations, not just limited to the horizontal plane. Through three-dimensional numerical simulations, this paper discusses the hydrodynamic characteristics and flow field structure of fish schools in various vertical patterns. The results show that a school of fish arranged vertically can improve the thrust and swimming efficiency of individuals as well as those arranged horizontally. There are two ways to significantly enhance hydrodynamic advantages. One is to maximize the channeling effect in multiple planes. In a vertical circular pattern, the fish school forms multiple coupled channels, which hinder the free expansion of flow in both vertical and horizontal planes, thereby obtaining higher energy-saving benefits. The other is the combined exploitation of the channeling effect and wake energy, which is illustrated in the vertical rectangular pattern. The following fish can use the channeling effect to increase the thrust due to the presence of parallel companion. Meanwhile, the high speed region of the following fish can merge with the jet flows of the preceding fish, thereby capturing the wake energy and further improving swimming efficiency.

A comprehensive review of hydrodynamic studies on fish schooling

“…Similarly, Oza et al (2019) observed that a 2D rectangular lattice formation offers the largest hydrodynamic benefit when compared to in-line, phalanx, and solitary swimmers. The results from these studies suggest that the combined utilization of the channeling effect and wake energy can achieve higher efficiency (Li et al 2021c).…”

“…Altering the schooling configuration into a rectangular/square or diamond configuration will alter the resulting hydrodynamic impacts. Studies using this configuration generally saw an increase in thrust and propulsive efficiency (Li et al 2021c) compared to a single fish. Daghooghi and Borazjani (2015) found that an individual fish in this schooling configuration could achieve up to a 20% higher cruising speed than a sole swimmer.…”

“…Coefficients c 1 and c 2 are linear and quadratic wave amplitude, respectively, and are typically determined from experimental observations of fish swimming. (Barrett 1996, Li et al 2021c.…”

“…Another critical factor to consider is the physical characteristics and the kinematic difference and variability of the submerged bodies. Typically, the pre-described motion of the hydrofoils used in the study matches that of a carangiform motion except for Novati et al (2017) and Wei et al (2022b), which used sub-carangiform, and Li et al (2021c), which utilized thunniform motion. One should consider the locomotion of the schooling members as it will impact the hydrodynamics interactions.…”

“…The total energy absorption efficiency increases in the range from 12% to 22% (Ma et al 2021). This two-member schooling arrangement is the primary focus of physical experimentation studies and is extensively examined in numerical simulations (Deng et al 2007, Kim et al 2010, Zhu et al 2014, Shoele and Zhu 2015, Tian 2015, Tian et al 2016, Novati et al 2017, Khalid et al 2018, Park and Sung 2018, Verma et al 2018, Han et al 2019, 2022, Newbolt et al 2019, 2022, Li et al 2019a, 2021c, Ma et al 2021, Wei et al 2022b.…”