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arxiv: 2604.22962 · v1 · submitted 2026-04-24 · ⚛️ physics.flu-dyn

On Fin Based Propulsion and Maneuvering for Uncrewed Underwater Vehicles

Parker Thomas Grobe This is my paper

Pith reviewed 2026-05-08 10:05 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords bio-inspired propulsionoscillating finsunderwater vehicleshydrodynamicsthrust enhancementphase offsetvortex interactionBayesian optimization
0
0 comments X

The pith

Tuning phase offsets and spacing in multi-fin setups enhances thrust by allowing energy extraction from wakes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper simulates oscillating fins inspired by aquatic animals to propel underwater vehicles. It finds that in systems with multiple fins, the timing between their oscillations and the distance between them determines whether the group produces more thrust or less. Proper coordination lets the rear fins use vortices from the front ones to gain extra push. This approach is tested with different motion patterns and a method to find the best settings quickly. If accurate, it offers a way to make uncrewed underwater vehicles more efficient and agile without traditional propellers.

Core claim

The central claim is that downstream fins in multi-fin configurations can extract energy from the vortex wakes of upstream fins through tuned phase offsets and spacing, leading to significantly enhanced thrust, as shown in two-dimensional simulations of NACA 0020 hydrofoils with prescribed heave and pitch motions, while poor timing reduces performance.

What carries the argument

The phase offset parameter that describes interactions in multi-fin systems, combined with the Boundary Data Immersion Method solver for incompressible flow, enables modeling of vortex interactions and energy recovery.

If this is right

  • Baseline single fin simulations establish force generation characteristics using Strouhal number.
  • Reduced order model with torsional spring emulates fin flexibility and generates net lateral forces for maneuvering via asymmetric actuation.
  • Bayesian optimization efficiently identifies high-performance multi-fin configurations in the large parameter space.
  • Multi-fin thrust can be enhanced or reduced depending on phase and spacing tuning.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Real vehicles might achieve better maneuverability by dynamically adjusting fin phases based on similar optimization.
  • This framework could extend to three-dimensional simulations to check if the energy extraction holds in more realistic flows.
  • Designers of underwater robots could use these insights to replace or supplement propeller systems with fin arrays.

Load-bearing premise

The two-dimensional incompressible simulations with prescribed rigid-body motions and a simple torsional spring accurately represent the complex three-dimensional, flexible, and unsteady hydrodynamics of real fins.

What would settle it

Three-dimensional experiments or higher-fidelity simulations of flexible multi-fin systems showing no net thrust increase from phase tuning compared to single fin or uncoordinated cases.

Figures

Figures reproduced from arXiv: 2604.22962 by Parker Thomas Grobe.

Figure 1.1
Figure 1.1. Figure 1.1: Computational domain schematic of our standard view at source ↗
Figure 1.2
Figure 1.2. Figure 1.2: Instantaneous coefficient of thrust, CT , for each fin in a N = 3 fin system over 10 oscillation cycles. 1.6 Temporal Resolution Study The next refinement considered the number of temporal data points saved per oscillation cycle. For baseline simulations, force data was recorded at 100 intervals per cycle. However, large parameter sweeps substantially increase storage requirements and post processing tim… view at source ↗
Figure 1.3
Figure 1.3. Figure 1.3: Instantaneous force in the x direction for each fin in a 3-fin system over the third oscillation cycle (t/T ∈ [0, 1]). Temporal resolution comparison between 33 saved points per cycle and 100 saved points per cycle view at source ↗
Figure 1.4
Figure 1.4. Figure 1.4: Grid refinement study showing relative error of system-average view at source ↗
Figure 1.5
Figure 1.5. Figure 1.5: Computational mesh comparison showing refinement from view at source ↗
Figure 1.6
Figure 1.6. Figure 1.6: Cycle-averaged coefficient of thrust, CT , for a single fin (NACA 0020) at our fine setting (c = 64 cells) as Strouhal number (St) varies. 23 view at source ↗
Figure 2.1
Figure 2.1. Figure 2.1: Comparison of two fundamental thrust-generation mechanisms for an os view at source ↗
Figure 2.2
Figure 2.2. Figure 2.2: A NACA 0020 undergoing combined pitch and heave motion. Kinematic view at source ↗
Figure 2.3
Figure 2.3. Figure 2.3: Kinematics and force generation for a single oscillating fin. In (a) prescribed view at source ↗
Figure 2.4
Figure 2.4. Figure 2.4: Comparison between a rigid (prescribed pitching) fin and a leading edge view at source ↗
Figure 3.1
Figure 3.1. Figure 3.1: Waveform comparison between a regular sinusoidally symmetric heave view at source ↗
Figure 3.2
Figure 3.2. Figure 3.2: Instantaneous θ comparison between symmetrically varying stiffness leading edge spring fin (case 1) and an asymmetric varying stiffness leading edge spring (case 2). 3.3.1 Lift-based contribution The lift force scales with the square of the effective velocity and the instanta￾neous lift coefficient. Following the scaling arguments, FL ∼ ρscU2 effCL, CL ∼ α + cα˙ Ueff (3.9) where s is the span, c is the c… view at source ↗
Figure 3.3
Figure 3.3. Figure 3.3: Mean side-force coefficient CL (black) and mean thrust coefficient CT (blue) as functions of imposed pitch bias for multiple pitch amplitudes θ0 = 0◦ , 5 ◦ , 10◦ , and 15◦ . Increasing pitch bias produces a linear rise in CL across all θ0 cases, consistent with the predicted linear scaling with θpb. Simultaneously, CT decreases as bias increases linearly as the bias angle grows. The slope of this increas… view at source ↗
Figure 3.4
Figure 3.4. Figure 3.4: Cycle averaged lateral force CL plotted against tilt factor λ for pure heave (θ0 = 0◦ ), a standard pitching and heaving fin (θ0 = 30◦ ), and a leading edge spring fin (θ0 = passive). allowing passive pitch. For the prescribed pitching case, the pitch waveform was also made asymmetric so that it followed the tilted heave motion. For the rigid configurations, the trend is clear. As the heave becomes more … view at source ↗
Figure 3.5
Figure 3.5. Figure 3.5: Coefficient of lateral force CL as a function of waveform asymmetry gener￾ated by the tilted heave motion. (a) CL plotted against the ratio of maximum heave speed during the upstroke and downstroke. (b) CL plotted against the ratio of peak heave acceleration between the two half strokes. on one half stroke, the resulting increase in lateral force produces a larger passive pitch deflection. That rotation … view at source ↗
Figure 3.6
Figure 3.6. Figure 3.6: Cycle average coefficient of lateral force view at source ↗
Figure 3.7
Figure 3.7. Figure 3.7: Collapse of the medium stiffness case (k = 1250) against the stiffness￾asymmetry scaling variable S(p) = ku ku+B − kd kd+B . The mean lift coefficient CL from simulation is plotted against the theoretical scaling parameter, with a linear fit yielding a correlation coefficient of R = 0.987, indicating a strong linear relationship. comparison tests the simulation results against the structure of the derive… view at source ↗
Figure 4.1
Figure 4.1. Figure 4.1: Example of a pressure field for a generic oscillating 2-fin system depicting view at source ↗
Figure 4.2
Figure 4.2. Figure 4.2: Example of two flow fields one without (b.i) and one with (b.ii) a vortex view at source ↗
Figure 4.3
Figure 4.3. Figure 4.3: Color contour performance map of the thrust of the downstream fin relative view at source ↗
Figure 4.4
Figure 4.4. Figure 4.4: The thrust of the downstream fin relative to the upstream fin in a 2-fin view at source ↗
Figure 4.5
Figure 4.5. Figure 4.5: Instantaneous coefficient of thrust CT (black) and coefficient of power CP (blue) for the downstream fin over the final oscillation cycle for a high-performance case. The upper panel (green) shows the moment of maximum thrust, the lower panel (red) corresponds to the minimum thrust condition. cycle and accompanied by representative flow field snapshots. As expected, the downstream fin in this configurati… view at source ↗
Figure 4.6
Figure 4.6. Figure 4.6: Instantaneous coefficient of thrust CT (black) and coefficient of power CP (blue) for the downstream fin over the final oscillation cycle for a low-performance case. The upper panel (green) shows the moment of maximum thrust, the lower panel (red) corresponds to the minimum thrust condition. 4.3 Conclusion In this chapter we examined the hydrodynamic interactions present in two-fin systems and demonstrat… view at source ↗
Figure 5.1
Figure 5.1. Figure 5.1: Color contour plot showing the system average coefficient of thrust view at source ↗
Figure 5.2
Figure 5.2. Figure 5.2: Instantaneous coefficient of thrust over the final oscillation cycle for two view at source ↗
Figure 5.3
Figure 5.3. Figure 5.3: Mean coefficient of thrust CT for each fin in a three-fin system as the phase offsets ϕ1,2 and ϕ1,3 are varied for three different fin spacings. Columns correspond to the thrust produced by fin 1 (a), fin 2 (b), and fin 3 (c), while rows correspond to spacings of S = 0.5c (i), S = 2c (ii), and S = 10c (iii). Red regions indicate higher thrust and blue regions indicate lower thrust. The maps illustrate th… view at source ↗
Figure 5.4
Figure 5.4. Figure 5.4: Relative thrust produced by downstream fins after applying the phase view at source ↗
Figure 5.5
Figure 5.5. Figure 5.5: Color contour plot showing the system average Froude efficiency view at source ↗
Figure 5.6
Figure 5.6. Figure 5.6: Instantaneous coefficient of power CP over the final oscillation cycle for two three-fin systems corresponding to the high and low efficiency configurations identified in figure 5.5. Column (a) shows the temporal variation in power for each fin for the high (a.i) and low (a.ii) cases, while panel (b) highlights selected flow-field snapshots corresponding to key points in the power cycle. 83 view at source ↗
Figure 6.1
Figure 6.1. Figure 6.1: Bayesian optimization surrogate model for the three-fin system thrust view at source ↗
Figure 6.2
Figure 6.2. Figure 6.2: Thrust and efficiency of N-fin systems optimized for thrust using sequential Bayesian optimization. Performance is normalized by the single-fin baseline. Red markers show the performance of a reference configuration where each additional fin was assigned the same phase offset (equal phase case). Representative flow-field snapshots for the optimized N = 6 case are shown at (b.i) t/T = 0.5 and (b.ii) t/T =… view at source ↗
Figure 6.3
Figure 6.3. Figure 6.3: Thrust and efficiency of N-fin systems optimized for efficiency using sequen￾tial Bayesian optimization. Performance is normalized by the single-fin baseline. Red markers show the equal phase reference configuration. Representative flow field snap￾shots for the optimized N = 6 case are shown at (b.i) t/T = 0.5 and (b.ii) t/T = 1.0. The efficiency optimized cases displayed a similar trend to thrust optimi… view at source ↗
Figure 6.4
Figure 6.4. Figure 6.4: Three-fin system with variable spacing and phase between fins optimized view at source ↗
read the original abstract

Bio-inspired propulsion using oscillating fins has gained attention for its potential to achieve high thrust, efficiency, and maneuverability. Many aquatic organisms generate propulsion through coordinated fin oscillations, and understanding these hydrodynamic mechanisms can inform the design of advanced underwater vehicles. A numerical framework is developed to simulate a NACA 0020 hydrofoil undergoing prescribed heave and pitch about the leading edge in a uniform freestream. Simulations are performed using WaterLily, a two-dimensional incompressible flow solver based on the Boundary Data Immersion Method (BDIM). Key kinematic parameters, frequency, heave amplitude, pitch amplitude, and phase offset, are characterized through nondimensional groups, primarily the Strouhal number. Reynolds number is held constant to isolate kinematic effects, while an additional parameter is introduced to describe phase driven interactions in multi fin systems. The study begins with a single fin to establish baseline force generation. A reduced order model incorporating a leading-edge torsional spring is then developed to emulate flexibility. The effects of asymmetric actuation, through heave speed, pitch bias, and stiffness variation, are also examined, demonstrating the generation of net lateral forces for maneuvering. Next multi-fin configurations investigated. Downstream fins interact with vortices shed by upstream fins, enabling energy extraction from the wake. Results show that tuning phase offsets and spacing can significantly enhance thrust, while poor timing reduces performance. To efficiently explore the growing parameter space, Bayesian optimization is applied to identify high performance configurations. This work provides insight into the hydrodynamic mechanisms of oscillating fin propulsion and establishes a framework for designing efficient, bio-inspired underwater propulsion systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript presents a 2D numerical study of bio-inspired oscillating fin propulsion for underwater vehicles using the Boundary Data Immersion Method (BDIM) implemented in WaterLily. It characterizes single NACA 0020 hydrofoils with prescribed heave and pitch motions, introduces a torsional spring model for leading-edge flexibility, explores asymmetric actuation for maneuvering, and investigates multi-fin configurations where phase offsets and spacing are optimized via Bayesian methods to enhance thrust through wake vortex interactions.

Significance. This research could inform the design of efficient and maneuverable uncrewed underwater vehicles by providing a framework for optimizing fin kinematics. The application of Bayesian optimization to explore the parameter space for multi-fin systems is a strength for efficiently identifying promising configurations. However, the significance is tempered by the preliminary nature of the 2D simulations without supporting validation or three-dimensional analysis.

major comments (3)
  1. [Results on multi-fin configurations] The statement that 'tuning phase offsets and spacing can significantly enhance thrust' lacks any reported quantitative values, such as thrust coefficients, percentage improvements, or comparisons to single-fin baselines, which are necessary to substantiate the central claim.
  2. [Numerical methods and validation] There is no mention of mesh convergence studies, grid independence tests, or validation against established benchmarks for oscillating hydrofoils (e.g., comparison of mean thrust or efficiency at given Strouhal numbers), undermining confidence in the simulation outputs that support all performance claims.
  3. [Multi-fin wake interaction analysis] The attribution of performance gains to energy extraction from upstream vortices in 2D simulations does not consider or test the impact of three-dimensional effects, such as tip vortices and spanwise flow, which could disrupt the wake structures and reduce or eliminate the reported benefits in actual three-dimensional fins.
minor comments (2)
  1. [Abstract] The abstract refers to 'an additional parameter' for phase-driven interactions in multi-fin systems without defining or naming it, which should be clarified for reader understanding.
  2. [Kinematic parameters] Consider providing a table listing all nondimensional groups (Strouhal number, etc.) and their explored ranges to improve clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed review of our manuscript. We appreciate the recognition of the potential applications to UUV design and the use of Bayesian optimization. We agree that the manuscript can be strengthened by providing explicit quantitative results, adding numerical validation details, and expanding the discussion of 2D limitations. We address each major comment below and will incorporate the necessary revisions.

read point-by-point responses

  1. Referee: The statement that 'tuning phase offsets and spacing can significantly enhance thrust' lacks any reported quantitative values, such as thrust coefficients, percentage improvements, or comparisons to single-fin baselines, which are necessary to substantiate the central claim.

    Authors: We agree that quantitative metrics are needed to substantiate the claim. The revised manuscript will include explicit reporting of thrust coefficients for the optimized multi-fin cases, percentage improvements relative to single-fin baselines, and direct comparisons, drawn from the simulation data already obtained. revision: yes

  2. Referee: There is no mention of mesh convergence studies, grid independence tests, or validation against established benchmarks for oscillating hydrofoils (e.g., comparison of mean thrust or efficiency at given Strouhal numbers), undermining confidence in the simulation outputs that support all performance claims.

    Authors: This omission is a valid concern. We will add a dedicated section on numerical methods that reports mesh convergence studies and grid independence tests. We will also include validation comparisons to established oscillating hydrofoil benchmarks from the literature, focusing on mean thrust and efficiency at relevant Strouhal numbers. revision: yes

  3. Referee: The attribution of performance gains to energy extraction from upstream vortices in 2D simulations does not consider or test the impact of three-dimensional effects, such as tip vortices and spanwise flow, which could disrupt the wake structures and reduce or eliminate the reported benefits in actual three-dimensional fins.

    Authors: We recognize that 2D simulations cannot capture three-dimensional effects such as tip vortices and spanwise flow. In the revised manuscript we will expand the discussion to explicitly acknowledge these limitations and their potential to alter wake interactions in 3D fins, while emphasizing that the 2D results isolate key mechanisms and identify configurations warranting future three-dimensional study. revision: partial

Circularity Check

0 steps flagged

No circularity: results are direct outputs of independent 2D flow simulations

full rationale

The paper reports thrust and maneuvering outcomes obtained by solving the incompressible Navier-Stokes equations via BDIM on prescribed rigid-body kinematics (heave/pitch) plus a leading-edge torsional spring. Strouhal number and phase/spacing parameters are standard nondimensional inputs chosen independently of the target force coefficients. Bayesian optimization is applied only as an efficient search algorithm over the simulation parameter space; it does not fit a model whose predictions are then fed back as the reported gains. No equations, fitted parameters, or self-citations are shown that reduce the claimed performance enhancements to quantities defined by the same data or by prior work of the same author. The derivation chain is therefore self-contained against external numerical benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

Abstract-only review limits visibility into specific assumptions; standard incompressible CFD and rigid-body kinematics appear to be used without new postulates.

free parameters (2)
  • Strouhal number
    Primary nondimensional parameter varied to characterize frequency and amplitude effects on force generation.
  • phase offset parameter for multi-fin systems
    Additional parameter introduced to describe timing interactions between fins.
axioms (1)
  • domain assumption Two-dimensional incompressible flow governed by Navier-Stokes equations
    Underlying assumption of the BDIM solver for hydrofoil motion in uniform freestream.

pith-pipeline@v0.9.0 · 5578 in / 1285 out tokens · 82124 ms · 2026-05-08T10:05:19.314004+00:00 · methodology

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Reference graph

Works this paper leans on

53 extracted references · 53 canonical work pages

  1. [1]

    S. Alben. Optimal flexibility of a flapping appendage in an inviscid fluid.Journal of Fluid Mechanics, 614:355–380, 2008

    work page 2008

  2. [2]

    Concept design of a flexible-hull unmanned undersea vehicle

    Jamie M Anderson, Michael S Triantafyllou, and Peter A Kerrebrock. Concept design of a flexible-hull unmanned undersea vehicle. InISOPE International Ocean and Polar Engineering Conference, pages ISOPE–I. ISOPE, 1997

    work page 1997

  3. [3]

    Bale et al

    R. Bale et al. Energy efficiency of swimming and flying animals.Proceedings of the National Academy of Sciences, 2014

    work page 2014

  4. [4]

    Bandyopadhyay

    P. Bandyopadhyay. Maneuvering hydrodynamics of fish and small underwater vehicles.Integrative and Comparative Biology, 2002

    work page 2002

  5. [5]

    Maneuvering hydrodynamics of fish and small un- derwater vehicles.Integrative and comparative biology, 42(1):102–117, 2002

    Promode R Bandyopadhyay. Maneuvering hydrodynamics of fish and small un- derwater vehicles.Integrative and comparative biology, 42(1):102–117, 2002

    work page 2002

  6. [6]

    Clark and A

    R. Clark and A. J. Smits. Thrust production and wake structure of a batoid- inspired oscillating fin.Journal of Fluid Mechanics, 822:408–430, 2017

    work page 2017

  7. [7]

    ¨Uber die partiellen differenzen- gleichungen der mathematischen physik.Mathematische annalen, 100(1):32–74, 1928

    Richard Courant, Kurt Friedrichs, and Hans Lewy. ¨Uber die partiellen differenzen- gleichungen der mathematischen physik.Mathematische annalen, 100(1):32–74, 1928

    work page 1928

  8. [8]

    Czarnowski, R

    J. Czarnowski, R. Cleary, and B. Kreamer. Exploring the possibility of placing traditional marine vessels under oscillating foil propulsion. InProceedings of the Seventh International Offshore and Polar Engineering Conference, International Offshore and Polar Engineering Conference, pages ISOPE–I–97–165, May 1997

    work page 1997

  9. [9]

    Dewey et al

    P. Dewey et al. Scaling laws for the thrust production of flexible pitching panels. Journal of Fluid Mechanics, 732:29–46, 2013

    work page 2013

  10. [10]

    F. Fish. Advantages of aquatic animals as models for bio-inspired drones.Bioin- spiration & Biomimetics, 2020

    work page 2020

  11. [11]

    Floryan, C

    D. Floryan, C. W. Rowley, and A. J. Smits. Scaling the propulsive performance of heaving and pitching foils.Journal of Fluid Mechanics, 822:386–397, 2017

    work page 2017

  12. [12]

    Floryan, T

    D. Floryan, T. Van Buren, and A. J. Smits. Efficient cruising for swimming and flying animals is dictated by fluid drag.Physical Review Fluids, 4:093102, 2019. 98

    work page 2019

  13. [13]

    Efficient cruising for swimming and flying animals is dictated by fluid drag.Proceedings of the National Academy of Sciences, 115(32):8116–8118, 2018

    Daniel Floryan, Tyler Van Buren, and Alexander J Smits. Efficient cruising for swimming and flying animals is dictated by fluid drag.Proceedings of the National Academy of Sciences, 115(32):8116–8118, 2018

    work page 2018

  14. [14]

    Gazzola, M

    M. Gazzola, M. Argentina, and L. Mahadevan. Scaling macroscopic aquatic loco- motion.Nature Physics, 10:758–761, 2014

    work page 2014

  15. [15]

    Vortex dynamics and fin-fin interactions result- ing in performance enhancement in fish-like propulsion.Physical Review Fluids, 8(7):073101, 2023

    Jiacheng Guo, Pan Han, Wei Zhang, Junshi Wang, George V Lauder, Valentina Di Santo, and Haibo Dong. Vortex dynamics and fin-fin interactions result- ing in performance enhancement in fish-like propulsion.Physical Review Fluids, 8(7):073101, 2023

    work page 2023

  16. [16]

    Heathcote and I

    S. Heathcote and I. Gursul. Flexible flapping airfoil propulsion.AIAA Journal, 2007

    work page 2007

  17. [17]

    Katz and D

    J. Katz and D. Weihs. Hydrodynamic propulsion by large amplitude oscillation of an airfoil with chordwise flexibility.Journal of Fluid Mechanics, 88:485–497, 1978

    work page 1978

  18. [18]

    Nonsinusoidal path optimization of a flapping airfoil.AIAA journal, 45(8):2075–2082, 2007

    Mustafa Kaya and Ismail H Tuncer. Nonsinusoidal path optimization of a flapping airfoil.AIAA journal, 45(8):2075–2082, 2007

    work page 2075

  19. [19]

    M. M. Koochesfahani. Vortical patterns in the wake of an oscillating foil.AIAA Journal, 27(9):1200–1205, 1989

    work page 1989

  20. [20]

    M. J. Lighthill. Aquatic animal propulsion of high hydromechanical efficiency. Journal of Fluid Mechanics, 44:265–301, 1970

    work page 1970

  21. [21]

    Computational analysis of vortex dynamics and performance enhance- ment due to body–fin and fin–fin interactions in fish-like locomotion.Journal of fluid mechanics, 829:65–88, 2017

    Geng Liu, Yan Ren, Haibo Dong, Otar Akanyeti, James C Liao, and George V Lauder. Computational analysis of vortex dynamics and performance enhance- ment due to body–fin and fin–fin interactions in fish-like locomotion.Journal of fluid mechanics, 829:65–88, 2017

    work page 2017

  22. [22]

    Michelin and S

    S. Michelin and S. Llewellyn Smith. Resonance and propulsion performance of a heaving flexible wing.Physics of Fluids, 2009

    work page 2009

  23. [23]

    Immersed boundary methods.Annu

    Rajat Mittal and Gianluca Iaccarino. Immersed boundary methods.Annu. Rev. Fluid Mech., 37(1):239–261, 2005

    work page 2005

  24. [24]

    Moored, P

    K. Moored, P. Dewey, A. Smits, and H. Haj-Hariri. Hydrodynamic wake reso- nance as an underlying principle of efficient unsteady propulsion.Journal of Fluid Mechanics, 708:329–348, 2012

    work page 2012

  25. [25]

    Muscutt, G

    L. Muscutt, G. Weymouth, and B. Ganapathisubramani. Performance augmen- tation mechanism of in-line tandem flapping foils.Journal of Fluid Mechanics, 827:484–505, 2017. 99

    work page 2017

  26. [26]

    Energy harvesting through flow-induced oscillations of a foil.Physics of fluids, 21(12), 2009

    Zhangli Peng and Qiang Zhu. Energy harvesting through flow-induced oscillations of a foil.Physics of fluids, 21(12), 2009

    work page 2009

  27. [27]

    Quinn, G

    D. Quinn, G. Lauder, and A. Smits. Scaling the propulsive performance of flexible foils.Journal of Fluid Mechanics, 2014

    work page 2014

  28. [28]

    D. B. Quinn, G. V. Lauder, and A. J. Smits. Scaling the propulsive performance of flexible heaving foils.Physical Review Fluids, 2:102101, 2017

    work page 2017

  29. [29]

    D. A. Read, F. S. Hover, and M. S. Triantafyllou. Forces on oscillating foils for propulsion and maneuvering.Ocean Engineering, 30:17–26, 2003

    work page 2003

  30. [30]

    Saadat et al

    M. Saadat et al. Hydrodynamic advantages of in-line schooling.Bioinspiration & Biomimetics, 2021

    work page 2021

  31. [31]

    J. O. Scherer. Experimental and theoretical investigation of large amplitude oscil- lation foil propulsion systems. Technical Report AD0673776, Hydronautics Inc., 1968

    work page 1968

  32. [32]

    Two- dimensional problems in hydrodynamics and aerodynamics, 1965

    Leonid Ivanovich Sedov, CK Chu, H Cohen, B Seckler, and J Gillis. Two- dimensional problems in hydrodynamics and aerodynamics, 1965

    work page 1965

  33. [33]

    Seo and R

    J. Seo and R. Mittal. Improved swimming performance via leading-edge vortex enhancement.Bioinspiration & Biomimetics, 2022

    work page 2022

  34. [34]

    A. J. Smits. Undulatory and oscillatory swimming.Journal of Fluid Mechanics, 874:1–14, 2019

    work page 2019

  35. [35]

    Tangorra et al

    J. Tangorra et al. Development of a biologically inspired propulsor for underwater vehicles.IEEE Journal of Oceanic Engineering, 2007

    work page 2007

  36. [36]

    G. K. Taylor, R. L. Nudds, and A. L. Thomas. Flying and swimming animals cruise at a strouhal number tuned for high power efficiency.Nature, 425:707–711, 2003

    work page 2003

  37. [37]

    Theodorsen and I

    T. Theodorsen and I. E. Garrick. Mechanism of flutter: A theoretical and exper- imental investigation of the flutter problem. Technical report, NACA, 1935

    work page 1935

  38. [38]

    M. S. Triantafyllou, G. S. Triantafyllou, and R. Gopalkrishnan. Wake mechanics for thrust generation in oscillating foils.Physics of Fluids, 5(12):2835–2837, 1993

    work page 1993

  39. [39]

    M. S. Triantafyllou, G. S. Triantafyllou, and D. K. P. Yue. Hydrodynamics of fishlike swimming.Annual Review of Fluid Mechanics, 32:33–53, 2000

    work page 2000

  40. [40]

    Van Buren, D

    T. Van Buren, D. Floryan, N. J. Wei, and A. J. Smits. Flow speed has little impact on propulsive characteristics of oscillating foils.Physical Review Fluids, 3:013102, 2018. 100

    work page 2018

  41. [41]

    Foil shapes for efficient fish-like propulsion

    Tyler Van Buren, Daniel Floryan, Ayodeji T Bode-Oke, Pan Han, Haibo Dong, and Alexander Smits. Foil shapes for efficient fish-like propulsion. InAIAA Scitech 2019 Forum, page 1379, 2019

    work page 2019

  42. [42]

    Scaling and performance of simultaneously heaving and pitching foils.AIAA Journal, 57(9):3666–3677, 2019

    Tyler Van Buren, Daniel Floryan, and Alexander J Smits. Scaling and performance of simultaneously heaving and pitching foils.AIAA Journal, 57(9):3666–3677, 2019

    work page 2019

  43. [43]

    Bioinspired underwater propulsors.Bioinspired structures and design, pages 113–139, 2020

    Tyler Van Buren, Daniel Floryan, and Alexander J Smits. Bioinspired underwater propulsors.Bioinspired structures and design, pages 113–139, 2020

    work page 2020

  44. [44]

    P. Webb. Maneuverability: general issues.IEEE Journal of Oceanic Engineering, 2004

    work page 2004

  45. [45]

    P. Webb. Stability and maneuverability.Fish Physiology, 2005

    work page 2005

  46. [46]

    Stability versus maneuvering: challenges for sta- bility during swimming by fishes.Integrative and Comparative Biology, 55(4):753– 764, 2015

    Paul W Webb and Daniel Weihs. Stability versus maneuvering: challenges for sta- bility during swimming by fishes.Integrative and Comparative Biology, 55(4):753– 764, 2015

    work page 2015

  47. [47]

    D. Weihs. Hydromechanics of fish schooling.Nature, 241:290–291, 1973

    work page 1973

  48. [48]

    A hydrodynamical analysis of fish turning manoeuvres.Proceedings of the Royal Society of London

    David Weihs. A hydrodynamical analysis of fish turning manoeuvres.Proceedings of the Royal Society of London. Series B. Biological Sciences, 182(1066):59–72, 1972

    work page 1972

  49. [49]

    Wen and G

    L. Wen and G. Lauder. Understanding undulatory locomotion in fishes.Bioinspi- ration & Biomimetics, 2013

    work page 2013

  50. [50]

    Weymouth and Bernat Font

    Gabriel D. Weymouth and Bernat Font. Waterlily.jl: A differentiable and backend- agnostic julia solver to simulate incompressible viscous flow and dynamic bodies, 2024

    work page 2024

  51. [51]

    Propulsive performance of oscillating plates with time-periodic flexibility.Journal of Fluid Mechanics, 959:A31, 2023

    David Yudin, Daniel Floryan, and Tyler Van Buren. Propulsive performance of oscillating plates with time-periodic flexibility.Journal of Fluid Mechanics, 959:A31, 2023

    work page 2023

  52. [52]

    Gen- erating maneuvering forces with oscillating propulsors

    David J Yudin, Ethan Watson, Daniel Floryan, and Tyler W Van Buren. Gen- erating maneuvering forces with oscillating propulsors. InAIAA SCITECH 2024 Forum, page 1557, 2024

    work page 2024

  53. [53]

    J. Zhou, J. H. Seo, and R. Mittal. Effect of schooling on flow generated sounds from carangiform swimmers.Bioinspiration & Biomimetics, 19(3), 2024. 101 Appendix A REDUCED-ORDER MODEL FOR A LEADING-EDGE SPRING FIN This appendix presents the derivation of the reduced-order dynamical model used to describe the passive pitching motion of a fin with a leading...

    work page 2024