@article{gray1936studies2,
    author = "Gray, J",
    title = "Studies in animal locomotion VI. The propulsive powers of the dolphin",
    year = "1936",
    journal = "Journal of Experimental Biology, v. 13, p. 192-199",
    note = "talkorigins\_source = {true}; raw\_reference = {Gray, J., 1936, Studies in animal locomotion VI. The propulsive powers of the dolphin: Journal of Experimental Biology, v. 13, p. 192-199.}"
}

@article{harris1936the,
    author = "Harris, J. E.",
    title = "The Role of the Fins in the Equilibrium of the Swimming Fish",
    year = "1936",
    journal = "Journal of Experimental Biology",
    abstract = "An attempt was made to determine the relationship of the fins to the equilibrium of the swimming dogfish. Two factors at least are involved in this equilibrium; passive mechanical forces and reflex motions of the fins themselves. The part played by the automatic (passive) components was estimated by experimenting on a model of Mustelus canis mounted in a wind tunnel tested at a suitable air speed. The equilibrium in the horizontal plane (yawing equilibrium--for turning movements) is unstable without fins, completely stable only in the absence of the first dorsal fin, and is neutral when all fins are present. In the vertical plane (pitching equilibrium--for rising and diving turns) the equilibrium is unstable without fins, and this instability is greatly increased by the presence of the pectorals. The pelvics have little or no effect. Stability and controllability are inversely related. The fish is comparatively stable in the horizontal plane, extremely controllable in the vertical plane. This fact is closely related to the flexibility of the body for lateral movements. The results obtained in the wind tunnel were confirmed by amputation of the fins of the living dogfish. The normal equilibrium of the swimming dogfish in the vertical plane is determined largely by the pectoral fins and the heterocercal tail. The relationship of these facts to the problem of the evolution of the swimming chordates is considered.",
    url = "https://doi.org/10.1242/jeb.13.4.476",
    doi = "10.1242/jeb.13.4.476",
    number = "4",
    pages = "476-493",
    volume = "13"
}

@article{harris1936the4,
    author = "Harris, J. E",
    title = "The role of fins in the equilibrium of the swimming fish I. Wind-tunnel tests on a model of Mustelus canis (Mitchill)",
    year = "1936",
    journal = "Journal of Experimental Biology, v. 13, p. 476-493",
    note = "talkorigins\_source = {true}; raw\_reference = {Harris, J. E., 1936, The role of fins in the equilibrium of the swimming fish I. Wind-tunnel tests on a model of Mustelus canis (Mitchill): Journal of Experimental Biology, v. 13, p. 476-493.}"
}

@article{s2311f2e98bb586470bb98f22751607918b3c08ffd,
    author = "Harris, J.",
    title = "The Role of the Fins in the Equilibrium of the Swimming Fish: I. Wind-Tunnel Tests on a Model of Mustelus canis (Mitchill)",
    year = "1936",
    journal = "The Journal of Experimental Biology",
    url = "https://www.semanticscholar.org/paper/311f2e98bb586470bb98f22751607918b3c08ffd",
    is_oa = "true",
    semanticscholar_citation_count = "149",
    semanticscholar_id = "311f2e98bb586470bb98f22751607918b3c08ffd"
}

@article{harris1938the,
    author = "Harris, J. E.",
    title = "The Role Of The Fins In The Equilibrium Of The Swimming Fish",
    year = "1938",
    journal = "Journal of Experimental Biology",
    abstract = "The paired fins of fishes are largely concerned with the production of vertical forces, and thus principally affect the pitching (rising and diving) equilibrium. In the sharks the pelvic fins increase to a small extent the static stability for pitching movements. Nevertheless, the relatively large area and forward position of the pectoral fins preponderates over the influence of the pelvics on the pitching stability, so that the contribution of the latter is very small. This is borne out by amputation experiments. In the bony fishes, the development of the actinopterygian fin leads to a much greater mobility of the fins. In consequence, the pelvic fins of the bony fishes exhibit a considerable adaptive radiation. In the percoid fishes the use of the pectoral fins as brakes produces a lift as well as a drag force. It is shown that the neutralization of this lift force by a downward force produced by the pelvic fins necessitates the forward migration of the latter. If this migration did not take place, the fish would either tilt upwards or rise bodily during the stop. The dynamical basis for this migration of the paired fins is considered in an approximate mathematical treatment of the equilibrium during the stop. This hypothesis is confirmed by amputation experiments, and also by the occurrence of a convergent fin migration in the Coelacanthidae. The absence of the forward pelvic fin migration in flying fishes also affords indirect support. There is no evidence to suggest that the pelvic fins can function as bilge keels, though they may be used actively to produce a rolling moment.",
    url = "https://doi.org/10.1242/jeb.15.1.32",
    doi = "10.1242/jeb.15.1.32",
    number = "1",
    pages = "32-47",
    volume = "15"
}

@article{harris1938the5,
    author = "Harris, J. E",
    title = "The role of fins in the equilibrium of the swimming fish II. The role of the pelvic fins",
    year = "1938",
    journal = "Journal of Experimental Biology, v. 13, p. 476-493",
    note = "talkorigins\_source = {true}; raw\_reference = {Harris, J. E., 1938, The role of fins in the equilibrium of the swimming fish II. The role of the pelvic fins: Journal of Experimental Biology, v. 13, p. 476-493.}"
}

@article{s28be9471ec5b36520a9bf7875592746d5b20a2dff,
    author = "Harris, J.",
    title = "The Role Of The Fins In The Equilibrium Of The Swimming Fish: II. The Role Of The Pelvic Fins",
    year = "1938",
    journal = "The Journal of Experimental Biology",
    url = "https://www.semanticscholar.org/paper/8be9471ec5b36520a9bf7875592746d5b20a2dff",
    is_oa = "true",
    semanticscholar_citation_count = "107",
    semanticscholar_id = "8be9471ec5b36520a9bf7875592746d5b20a2dff"
}

@misc{gray1957how3,
    author = "Gray, J",
    title = "How fishes swim",
    year = "1957",
    howpublished = "Scientific American, v. 197, p. 48-54",
    note = "talkorigins\_source = {true}; raw\_reference = {Gray, J., 1957, How fishes swim: Scientific American, v. 197, p. 48-54.}"
}

@article{doi1023071440000,
    author = "Robins, C. R.",
    title = "Studies on Fishes of the Family Ophidiidae: VI. Two New Genera and a New Species from American Waters",
    year = "1961",
    journal = "Copeia",
    url = "https://www.semanticscholar.org/paper/e01d1351f6ea7272b7d9b8fb29bbf83b68de9615",
    doi = "10.2307/1440000",
    is_oa = "true",
    number = "2",
    pages = "212",
    semanticscholar_citation_count = "5",
    semanticscholar_id = "e01d1351f6ea7272b7d9b8fb29bbf83b68de9615",
    volume = "1961"
}

@article{wu1971hydromechanics,
    author = "Wu, T. Yao-Tsu",
    title = "Hydromechanics of swimming propulsion. Part 3. Swimming and optimum movements of slender fish with side fins",
    year = "1971",
    journal = "Journal of Fluid Mechanics",
    abstract = "This paper seeks to evaluate the swimming flow around a typical slender fish whose transverse cross-section to the rear of its maximum span section is of a lenticular shape with pointed edges, such as those of spiny fins, so that these side edges are sharp trailing edges, from which an oscillating vortex sheet is shed to trail the body in swimming. The additional feature of shedding of vortex sheet makes this problem a moderate generalization of the paper on the swimming of slender fish treated by Lighthill (1960 a). It is found here that the propulsive thrust depends not only on the virtual mass of the tail-end section, but also on an integral effect of variations of the virtual mass along the entire body segment containing the trailing side edges, and that this latter effect can greatly enhance the thrust-making. The optimum shape problem considered here is to determine the transverse oscillatory movements a slender fish can make which will produce a prescribed thrust, so as to overcome the frictional drag, at the expense of the minimum work done in maintaining the motion. The solution is for the fish to send a wave down its body at a phase velocity c somewhat greater than the desired swimming speed U, with an amplitude nearly uniform from the maximum span section to the tail. Both the ratio U/c and the optimum efficiency are found to depend upon two parameters: the reduced wave frequency and a ‘proportionalloading parameter’, the latter being proportional to the thrust coefficient and to the inverse square of the wave amplitude. The basic mechanism of swimming is examined in the light of the principle of action and reaction by studying the vortex wake generated by the optimum movement.",
    url = "https://doi.org/10.1017/s0022112071000697",
    doi = "10.1017/s0022112071000697",
    number = "3",
    pages = "545-568",
    volume = "46"
}

@article{blight1977the1,
    author = "Blight, A. R",
    title = "The muscular control of vertebrate swimming motions",
    year = "1977",
    journal = "Biological Reviews, v. 52, p. 181-218",
    note = "talkorigins\_source = {true}; raw\_reference = {Blight, A. R., 1977, The muscular control of vertebrate swimming motions: Biological Reviews, v. 52, p. 181-218.}"
}

@book{videler1993fish,
    author = "Videler, John J.",
    title = "Fish Swimming",
    year = "1993",
    url = "https://doi.org/10.1007/978-94-011-1580-3",
    doi = "10.1007/978-94-011-1580-3"
}

@article{doi101017cbo9780511983641004,
    author = "Hoar, J. and Sim, E. and Webber, D. and O'dor, R.",
    title = "Mechanics and Physiology of Animal Swimming: The role of fins in the competition between squid and fish",
    year = "1994",
    booktitle = "The Mechanics and Physiology of Animal Swimming",
    url = "https://www.semanticscholar.org/paper/11dae0bc1f792f63534e765b3242e7f288aaec08",
    doi = "10.1017/CBO9780511983641.004",
    is_oa = "true",
    pages = "27-44",
    semanticscholar_citation_count = "63",
    semanticscholar_id = "11dae0bc1f792f63534e765b3242e7f288aaec08"
}

@incollection{christopher2010the,
    author = "Christopher, J. Fulton",
    title = "The Role of Swimming in Reef Fish Ecology",
    year = "2010",
    booktitle = "Fish Locomotion",
    url = "https://doi.org/10.1201/b10190-12",
    doi = "10.1201/b10190-12",
    pages = "374-406"
}

@article{wang2012multimodal,
    author = "Wang, Ming and Yu, JunZhi and Tan, Min and Zhang, JianWei",
    title = "Multimodal swimming control of a robotic fish with pectoral fins using a CPG network",
    year = "2012",
    journal = "Chinese Science Bulletin",
    url = "https://doi.org/10.1007/s11434-012-5005-6",
    doi = "10.1007/s11434-012-5005-6",
    number = "10",
    pages = "1209-1216",
    volume = "57"
}

@article{xu2012numerical,
    author = "Xu, Yi-gang and Wan, De-cheng",
    title = "Numerical Simulation of Fish Swimming with Rigid Pectoral Fins",
    year = "2012",
    journal = "Journal of Hydrodynamics",
    url = "https://doi.org/10.1016/s1001-6058(11)60243-6",
    doi = "10.1016/s1001-6058(11)60243-6",
    number = "2",
    pages = "263-272",
    volume = "24"
}

@misc{zhong2021fluidstructure,
    author = "Zhong, Qiang",
    title = "Fluid-Structure Interactions and Active Control in High-Performance Thunniform Swimming",
    year = "2021",
    publisher = "University of Virginia",
    abstract = "In terms of bulk swimming metrics such as speed, efficiency, maneuverability, and stealth, fishes vastly outperform human-made underwater vehicles.  Motivated by this performance gap, this thesis uses both idealized models of propulsors and reduced-order three-dimensional robotic platforms to distill the essential physics and design features of high-performance swimming. 
A unique wireless experimental system was developed at the beginning as the foundation of this thesis.  This experimental system has the ability to perform automatic direct force measurements and dynamic position tracking, which creates a bridge between traditional tethered tests and autonomous platforms. The modularized design allows us to configure the experimental system with different hardware add-ons and software for various studies.  Together with the newly developed Three-Dimensional Particle Image Velocimetry (3D PIV) system,  this experimental system is able to couple hydrodynamic features with performance measurements, thereby offering a powerful tool for studies in this thesis. 
When fishes/robots swim near the substrate or near each other, they introduce unsteady interactions with the boundary.  Both dynamic position tracking and direct force measurements reveal that unsteady steady ground effect leads to asymmetric lift generation and a boost in thrust without efficiency loss.   For the first time,  we proved the existence of equilibrium altitudes.  When close to the ground, the time-averaged lift is zero at certain altitudes and acts to return the foil to these equilibria. When the foil moves very close to the ground (d/c≤0.35), there exists another unstable equilibrium altitude that pushes the foil away from or towards the ground. In all cases, the stable equilibrium altitudes move higher with increasing Strouhal number or with decreasing reduced frequency, but the unstable equilibrium altitudes are less sensitive.  Increasing aspect ratio leads to stronger unsteady effects, including a stronger thrust boost, a larger asymmetric force, and a higher stable equilibrium altitude.  The inviscid nature of these phenomena indicates that similar effects might exist when swimming near another out-of-phase swimmer. 
Besides high-efficiency steady swimming,  fishes are highly maneuverable compared to man-made underwater vehicles.   Maneuvers are inherently transient,  so they are often studied via observations of fish and fish-like robots, where their dynamics cannot be recorded directly.  In the case of the fish-inspired maneuver study, we present a set of experiments in which a semi-autonomous hydrofoil performs repeatable in-plane maneuvers in a water tunnel.  We show that modulating the hydrofoil’s frequency, amplitude, pitch bias,  and stroke speed ratio produce streamwise and lateral maneuvers with mixed effectiveness.   Our findings provide a framework for considering in-plane maneuvers and streamwise/lateral trajectory corrections in fish and fish-inspired robots.
Most fishes are equipped with multiple fins that can be used for manipulating unsteady three-dimensional interactions. In the case of multi-fin interactions during fish swimming, our study revealed the importance of dorsal fin shape on swimming performance enhancement and its role in multi-fin interactions.   In particular,  we used a  tuna-inspired fish model with variable fin sharpness to study the interaction between elongated dorsal/analfins and caudal fins.  We found that the performance enhancement is stronger than previously thought (15\%increase in swimming speed and50\%increase in swimming economy)and is governed by a three-dimensional dorsal-fin-induced cross-flow that lowers the angle of attack on the caudal fin and promotes spanwise flow.  Both simulations and multi-layer particle image velocimetry reveal that the cross-flow stabilizes the leading-edge vortex on the caudal fin, similar to how wing strakes prevent stall during fixed-wing aircraft maneuvers.   Unlike other fin–fin interactions,  this mechanism is phase-insensitive and offers a simple, passive solution for flow control over oscillating propulsors.
Since flexible elements are widely present in fishes, it is reasonable to expect that flexibility might be relevant to their high swimming performance over a wide range of speeds. In the case of tail flexibility, we reveal one of the secrets of high fish efficiencies: tunable flexibility.  Motivated by fish, who use muscles to modulate their stiffness, we derived a model that explains how and why tuning stiffness affects performance.  We show that to maximize efficiency, muscle tension should scale with swimming speed squared, offering a simple tuning strategy for fish and fish-like robots. Tuning stiffness can double swimming efficiency at tuna-like frequencies and speeds (0-6 Hz; 0-2 body lengths/sec). Energy savings increase with frequency, suggesting that high-frequency fish and robots have the most to gain from tuning stiffness.
",
    url = "https://libraetd.lib.virginia.edu/public\_view/z890rv07b",
    doi = "10.18130/sdt3-y768"
}

@article{doi103390biomimetics7020045,
    author = "Menzer, Alec and Gong, Yuchen and Fish, F. and Dong, Haibo",
    title = "Bio-Inspired Propulsion: Towards Understanding the Role of Pectoral Fin Kinematics in Manta-like Swimming",
    year = "2022",
    journal = "Biomimetics",
    abstract = "Through computational fluid dynamics (CFD) simulations of a model manta ray body, the hydrodynamic role of manta-like bioinspired flapping is investigated. The manta ray model motion is reconstructed from synchronized high-resolution videos of manta ray swimming. Rotation angles of the model skeletal joints are altered to scale the pitching and bending, resulting in eight models with different pectoral fin pitching and bending ratios. Simulations are performed using an in-house developed immersed boundary method-based numerical solver. Pectoral fin pitching ratio (PR) is found to have significant implications in the thrust and efficiency of the manta model. This occurs due to more optimal vortex formation and shedding caused by the lower pitching ratio. Leading edge vortexes (LEVs) formed on the bottom of the fin, a characteristic of the higher PR cases, produced parasitic low pressure that hinders thrust force. Lowering the PR reduces the influence of this vortex while another LEV that forms on the top surface of the fin strengthens it. A moderately high bending ratio (BR) can slightly reduce power consumption. Finally, by combining a moderately high BR = 0.83 with PR = 0.67, further performance improvements can be made. This enhanced understanding of manta-inspired propulsive mechanics fills a gap in our understanding of the manta-like mobuliform locomotion. This motivates a new generation of manta-inspired robots that can mimic the high speed and efficiency of their biological counterpart.",
    url = "https://www.mdpi.com/2313-7673/7/2/45/pdf?version=1650248244",
    doi = "10.3390/biomimetics7020045",
    is_oa = "true",
    number = "2",
    pages = "45",
    semanticscholar_citation_count = "49",
    semanticscholar_id = "437e8995de228bc4d195febb8d9300882e8f00c7",
    volume = "7"
}

@article{doi101017jfm2023203,
    author = "Jeong, Young Dal and Kim, M. and Lee, Jae Hwa",
    title = "Intermittent swimming of two self-propelled flexible fins with laterally constrained heaving motions in a side-by-side configuration",
    year = "2023",
    journal = "Journal of Fluid Mechanics",
    abstract = "Abstract Inspired by the intermittent locomotion of fish schools, numerical simulations are performed with two self-propelled flexible fins in a side-by-side configuration with anti-phase oscillation actuated by laterally constrained heaving motions. For an intermittent swimming gait, one type of the half-tail-beating mode (HT mode) and two types of multiple-tail-beating modes coasting at the smallest (MTS mode) and largest (MTL mode) lateral gap distances are applied. Similar to the continuous-tail-beating mode (CT mode), equilibrium lateral gap distances between two fins with HT and MTL modes exist, whereas two fins with MTS mode do not maintain a lateral equilibrium state. Although the cycle-averaged lateral force acting on two fins with CT and MTL modes is mostly determined by an outward deflected jet and enhanced positive pressure between two fins, an added-mass lateral force related to an asymmetric flapping kinematics by passive flexibility also plays an important role in MTL mode to achieve a stable state with a lateral gap distance smaller than that in CT mode. When the cruising speed or the cycle-averaged input power is identical in a stable state, the cost of transport (COT) for two fins with MTL mode is smaller than that with CT mode due to not only a benefit from the intermittent swimming gait but also an enhanced schooling benefit with a small equilibrium lateral gap distance. The COT for two fins with CT mode is reduced further when the bending rigidity increases, whereas it is opposite with MTL mode.",
    url = "https://www.semanticscholar.org/paper/804e6e456197ce80dabe4bc12dea177917b86671",
    doi = "10.1017/jfm.2023.203",
    is_oa = "true",
    semanticscholar_citation_count = "11",
    semanticscholar_id = "804e6e456197ce80dabe4bc12dea177917b86671",
    volume = "960"
}

@article{li2023the,
    author = "Li, Yuhan and Song, Jialei and Zhong, Yong and Yin, Bo",
    title = "The roles of fish median fins on the hydrodynamics and muscle actuation in carangiform swimming",
    year = "2023",
    journal = "Journal of Fluids and Structures",
    url = "https://doi.org/10.1016/j.jfluidstructs.2023.104000",
    doi = "10.1016/j.jfluidstructs.2023.104000",
    pages = "104000",
    volume = "123"
}

@article{doi101115imece2024145558,
    author = "Guo, Jiacheng and Dong, Haibo",
    title = "Hydrodynamics of Active Fin Control in Fish-Like Swimming",
    year = "2024",
    journal = "Volume 8: Fluids Engineering",
    booktitle = "Volume 8: Fluids Engineering",
    abstract = "Median fins have been found to enhance the forward propulsion in fish-like swimming, by enhancing the caudal-fin (CF) thrust through fin-fin interaction and reducing trunk (TK) drag through body-fin interaction. For stability or performance reasons, many fish-like robots have adopted dorsal fins in their designs. There has also been growing interest in emulating the individual opening and closing of the median fins (fanning motion), observed in nature, in bio-inspired underwater vehicle designs. The current study analyzes the effect of periodic fanning of the dorsal fin (DF) on the performance of fish-like swimming, in terms of thrust production and power consumption. Using a trout-like model on which strong fin-fin interaction was discovered, periodic fanning motion of the DF has been introduced, and direct-numerical simulations (DNS) are conducted. An immersed-boundary method (IBM) is used to resolve the body shape and motion of the trout-like model. The fanning phase relative to the start of the undulating cycle is varied from 0 to 360° in increments of 60°. Regardless of the fanning phase, the hydrodynamic power is always saved compared to the absence of fanning motion. Given a fanning phase (ϕf) of 60°, the power is saved the most, though similarly forward force is reduced on the body as a whole. At ϕf = 240°, the forward force is improved compared to the no-fanning case, with a slightly reduced hydrodynamic power. It is found that at this ϕf, viscous drag on the DF is reduced given its periodic reduction of surface area, while its role as vortex generator is still fulfilled, so that the effectiveness of fin-fin interaction in enhancing CF thrust is preserved.",
    url = "https://www.semanticscholar.org/paper/9d78e40983cf5ce4c95b3280612e2a710fcdc480",
    doi = "10.1115/imece2024-145558",
    is_oa = "true",
    semanticscholar_id = "9d78e40983cf5ce4c95b3280612e2a710fcdc480"
}

@article{doi103390biomimetics9010045,
    author = "Macías, M. M. and García-Ortiz, J. H. and Oliveira, T. and Júnior, A. C. P. Brasil",
    title = "Numerical Investigation of Dimensionless Parameters in Carangiform Fish Swimming Hydrodynamics",
    year = "2024",
    journal = "Biomimetics",
    abstract = "Research into how fish and other aquatic organisms propel themselves offers valuable natural references for enhancing technology related to underwater devices like vehicles, propellers, and biomimetic robotics. Additionally, such research provides insights into fish evolution and ecological dynamics. This work carried out a numerical investigation of the most relevant dimensionless parameters in a fish swimming environment (Reynolds Re , Strouhal St , and Slip numbers) to provide valuable knowledge in terms of biomechanics behavior. Thus, a three-dimensional numerical study of the fish-like lambari, a BCF swimmer with carangiform kinematics, was conducted using the URANS approach with the k- ω -SST transition turbulence closure model in the OpenFOAM software. In this study, we initially reported the equilibrium Strouhal number, which is represented by St∗ , and its dependence on the Reynolds number, denoted as Re . This was performed following a power–law relationship of St∝Re(−α) . We also conducted a comprehensive analysis of the hydrodynamic forces and the effect of body undulation in fish on the production of swimming drag and thrust. Additionally, we computed propulsive and quasi-propulsive efficiencies, as well as examined the influence of the Reynolds number and Slip number on fish performance. Finally, we performed a vortex dynamics analysis, in which different wake configurations were revealed under variations of the dimensionless parameters St , Re , and Slip . Furthermore, we explored the relationship between the generation of a leading-edge vortex via the caudal fin and the peak thrust production within the motion cycle.",
    url = "https://www.mdpi.com/2313-7673/9/1/45/pdf?version=1704983686",
    doi = "10.3390/biomimetics9010045",
    is_oa = "true",
    number = "1",
    pages = "45",
    semanticscholar_citation_count = "8",
    semanticscholar_id = "bb344a4a83664b0724e6597c1a905970c18345b5",
    volume = "9"
}

@article{menzer2026fins,
    author = "Menzer, Alec and Pan, Yu and Lauder, George V and Dong, Haibo",
    title = "Fins in formation: hydrodynamic impact of median fins in in-line fish swimming",
    year = "2026",
    journal = "Bioinspiration \& Biomimetics",
    abstract = "Median fins, including the dorsal and anal fins, influence fish propulsion by lowering body drag and increasing caudal fin thrust through active movement. While their role in solitary swimming is established, their impact on hydrodynamics within schooling environments remains unclear. Using high-fidelity computational fluid dynamics simulations of in-line fish pairs, we systematically varied median fin presence on leaders and followers to isolate neighbor-induced performance changes. When comparing the full-finned configuration to the finless configuration at a leader-follower streamwise spacing (S) of 1.1 body lengths (l), the follower’s drag was reduced by 9.5\%. A significant contribution of the total drag reduction, about 70\%, was neighbor-induced, arising from wake-body interactions with the wake of a leader that had median fins, while the rest was attributed to adding the follower’s own median fins. This neighbor-induced benefit arises from stronger leader-generated vortex structures that interact with the follower’s body, lowering both shear and pressure drag. The neighbor-induced benefits persist across a range of spacings, diminishing only beyond S = 1.4 l. At higher Reynolds numbers, the neighbor-induced drag reduction also dominates the total drag reduction of the follower. These findings reveal that median fins can serve as hydrodynamic tools for enhancing group swimming performance through neighbor-induced effects, extending their recognized functional role beyond self-induced improvements in solitary swimming.",
    url = "https://doi.org/10.1088/1748-3190/ae3652",
    doi = "10.1088/1748-3190/ae3652",
    number = "1",
    pages = "016013",
    volume = "21"
}