Hostname: page-component-669899f699-b58lm Total loading time: 0 Render date: 2025-04-25T02:26:33.777Z Has data issue: false hasContentIssue false
  • English
  • Français

How shape and flapping rate affect the distribution of fluid forces on flexible hydrofoils

Published online by Cambridge University Press:  19 August 2020

Paule Dagenais Open the ORCID record for Paule Dagenais [Opens in a new window]  and
Christof M. Aegerter Open the ORCID record for Christof M. Aegerter [Opens in a new window]
Paule Dagenais
Affiliation:
Physik-Institut, University of Zurich, Winterthurerstrasse 190, 8057Zurich, Switzerland
Christof M. Aegerter*
Affiliation:
Physik-Institut, University of Zurich, Winterthurerstrasse 190, 8057Zurich, Switzerland
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We address the fluid–structure interaction of flexible fin models oscillating in a water flow. Here, we investigate in particular the dependence of hydrodynamic force distributions on fin geometry and flapping frequency. For this purpose, we employ state-of-the-art techniques in pressure evaluation to describe fluid force maps with high temporal and spatial resolution on the deforming surfaces of the hydrofoils. Particle tracking velocimetry is used to measure the three-dimensional fluid velocity field, and the hydrodynamic stress tensor is subsequently calculated based on the Navier–Stokes equation. The shape and kinematics of the fin-like foils are linked to their ability to generate propulsive thrust efficiently, as well as the accumulation of external contact forces and the resulting internal tension throughout a flapping cycle.

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 901 , 25 October 2020 , A1
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Affleck, R. J. 1950 Some points in the function, development and evolution of the tail in fishes. Proc. Zool. Soc. Lond. 120 (2), 349–368.CrossRefGoogle Scholar
Aris, R. 1990 Vectors, Tensors and the Basic Equations of Fluid Mechanics. Dover.Google Scholar
Arnal, D. 1984 Description and prediction of transition in two-dimensional, incompressible flow. In Special Course on Stability and Transition of Laminar Flow (ed. AGARD-R-709). Defense Technical Information Center.Google Scholar
Bainbridge, R. 1960 Speed and stamina in three fish. J. Expl Biol. 37 (1), 129–153.Google Scholar
Baur, T. & Köngeter, J. 1999 PIV with high temporal resolution for the determination of local pressure reductions from coherent turbulence phenomena. In 3rd International Workshop on PIV, Santa Barbara, USA, pp. 101–106.Google Scholar
Blake, R. W., Li, J. & Chan, K. H. S. 2009 Swimming in four goldfish Carassius auratus morphotypes: understanding functional design and performance employing artificially selected forms. J. Fish Biol. 75 (3), 591–617.CrossRefGoogle ScholarPubMed
Blickhan, R., Krick, C., Zehren, D., Nachtigall, W. & Breithaupt, T. 1992 Generation of a vortex chain in the wake of a suhundulatory swimmer. Naturwissenschaften 79, 220–221.CrossRefGoogle Scholar
Bohl, D. G. & Koochesfahani, M. M. 2009 MTV measurements of the vortical field in the wake of an airfoil oscillating at high reduced frequency. J. Fluid Mech. 620, 63–88.CrossRefGoogle Scholar
Bohlen, J., Petrtyl, M., Petra, C. & Chhouk, B. 2016 Schistura kampucheensis, a new species of loach from Cambodia (Teleostei: Nemacheilidae). Ichthyol. Expl Freshwat. 26, 353–362.Google Scholar
Bozkurttas, M., Dong, H., Mittal, R., Madden, P. & Lauder, G. V. 2006 Hydrodynamic performance of deformable fish fins and flapping foils. In 44th AIAA Aerospace Sciences Meeting and Exhibit. Available at: https://arc.aiaa.org/doi/pdf/10.2514/6.2006-1392.CrossRefGoogle Scholar
Bozkurttas, M., Mittal, R., Dong, H., Lauder, G. V. & Madden, P. 2009 Low-dimensional models and performance scaling of a highly deformable fish pectoral fin. J. Fluid Mech. 631, 311–342.CrossRefGoogle Scholar
Buchholz, J. & Smits, A. 2006 On the evolution of the wake structure produced by a low-aspect-ratio pitching panel. J. Fluid Mech. 564, 433–443.Google Scholar
Dabiri, J. O., Bose, S., Gemmell, B., Colin, S. & Costello, J. 2014 An algorithm to estimate unsteady and quasi-steady pressure fields from velocity field measurements. J. Expl Biol. 217, 331–336.CrossRefGoogle ScholarPubMed
Dagenais, P. & Aegerter, C. M. 2019 Hydrodynamic stress maps on the surface of a flexible fin-like foil. arXiv:1910.09887.Google Scholar
Dai, H., Luo, H., Ferreira de Sousa, P. & Doyle, J. 2012 Thrust performance of a flexible low-aspect-ratio pitching plate. Phys. Fluids 24, 101903.CrossRefGoogle Scholar
David, L., Jardin, T., Braud, P. & Farcy, A. 2012 Time-resolved scanning tomography PIV measurements around a flapping wing. Exp. Fluids 52 (4), 857–864.CrossRefGoogle Scholar
David, M. J., Govardhan, R. N. & Arakeri, J. H. 2017 Thrust generation from pitching foils with flexible trailing edge flaps. J. Fluid Mech. 828, 70–103.CrossRefGoogle Scholar
Dewey, P., Boschitsch, B., Moored, K., Stone, H. & Smits, A. 2013 Scaling laws for the thrust production of flexible pitching panels. J. Fluid Mech. 732, 29–46.CrossRefGoogle Scholar
Dewey, P. A., Carriou, A. & Smits, A. J. 2012 On the relationship between efficiency and wake structure of a batoid-inspired oscillating fin. J. Fluid Mech. 691, 245–266.CrossRefGoogle Scholar
Dracos, Th. 1996 Particle Tracking Velocimetry (PTV), pp. 155–160. Springer Netherlands.Google Scholar
Drucker, E. G. & Lauder, G. V. 1999 Locomotor forces on a swimming fish: three-dimensional vortex wake dynamics quantified using digital particle image velocimetry. J. Expl Biol. 202 (18), 2393–2412.Google ScholarPubMed
Drucker, E. G. & Lauder, G. V. 2001 Locomotor function of the dorsal fin in teleost fishes: experimental analysis of wake forces in sunfish. J. Expl Biol. 204 (17), 2943–2958.Google ScholarPubMed
Drucker, E. G. & Lauder, G. V. 2005 Locomotor function of the dorsal fin in rainbow trout: kinematic patterns and hydrodynamic forces. J. Expl Biol. 208 (23), 4479–4494.CrossRefGoogle ScholarPubMed
Egan, B., Brownell, C. & Murray, M. 2016 Experimental assessment of performance characteristics for pitching flexible propulsors. J. Fluids Struct. 67, 22–33.CrossRefGoogle Scholar
Eloy, C. 2012 Optimal Strouhal number for swimming animals. J. Fluids Struct. 30, 205–218.CrossRefGoogle Scholar
Eloy, C. 2013 On the best design for undulatory swimming. J. Fluid Mech. 717, 48–89.CrossRefGoogle Scholar
Esposito, C. J., Tangorra, J. L., Flammang, B. E. & Lauder, G. V. 2012 A robotic fish caudal fin: effects of stiffness and motor program on locomotor performance. J. Expl Biol. 215 (1), 56–67.CrossRefGoogle ScholarPubMed
Feilich, K. L. & Lauder, G. V. 2015 Passive mechanical models of fish caudal fins: effects of shape and stiffness on self-propulsion. Bioinspir. Biomim. 10, 036002.CrossRefGoogle ScholarPubMed
Flammang, B. E., Lauder, G. V., Troolin, D. & Strand, T. E. 2011 a Volumetric imaging of fish locomotion. Biol. Lett. 7, 695–8.CrossRefGoogle ScholarPubMed
Flammang, B. E., Lauder, G. V., Troolin, D. & Strand, T. E. 2011 b Volumetric imaging of shark tail hydrodynamics reveals a three-dimensional dual-ring vortex wake structure. Proc. R. Soc. B/Biol. Sci. 278, 3670–3678.CrossRefGoogle ScholarPubMed
Floryan, D., Van Buren, T., Rowley, C. & Smits, A. 2017 Scaling the propulsive performance of heaving and pitching foils. J. Fluid Mech. 822, 386–397.CrossRefGoogle Scholar
Fujisawa, N., Nakamura, Y., Matsuura, F. & Sato, Y. 2006 Pressure field evaluation in microchannel junction flows through $\mathrm {\mu }$PIV measurement. Microfluid Nanofluid 2 (5), 447–453.CrossRefGoogle Scholar
Geerlink, P. J. & Videler, J. 1986 The relation between structure and bending properties of teleost fin rays. Neth. J. Zool. 37, 59–80.Google Scholar
Godoy-Diana, R., Aider, J. L. & Wesfreid, J. 2008 Transitions in the wake of a flapping foil. Phys. Rev. E: Stat. Nonlinear Soft Matter Phys. 77, 016308.CrossRefGoogle ScholarPubMed
Green, M. A., Rowley, C. W., Smits, A. J. 2011 The unsteady three-dimensional wake produced by a trapezoidal pitching panel. J. Fluid Mech. 685, 117–145.CrossRefGoogle Scholar
Gresho, P. M. & Sani, R. L. 1987 On pressure boundary conditions for the incompressible Navier–Stokes equations. Intl J. Numer. Meth. Fluids 7 (10), 1111–1145.CrossRefGoogle Scholar
Gurka, R., Liberzon, A., Hefetz, D., Rubinstein, D. & Shavit, U. 1999 Computation of pressure distribution using PIV velocity data. In Third International Workshop on PIV, Santa Barbara, CA, pp. 671–676..Google Scholar
Incropera, F. P., Dewitt, D. P., Bergman, T. L. & Lavine, A. S. 2007 Fundamentals of Heat and Mass Transfer, 6th edn. Wiley.Google Scholar
Jakobsen, M., Dewhirst, T. & Greated, C. 1999 Particle image velocimetry for predictions of acceleration fields and force within fluid flows. Meas. Sci. Technol. 8, 1502.CrossRefGoogle Scholar
Jardin, T., David, L. & Farcy, A. 2009 Characterization of vortical structures and loads based on time-resolved PIV for asymmetric hovering flapping flight. Exp. Fluids 46, 847–857.CrossRefGoogle Scholar
Joshi, P., Liu, X. & Katz, J. 2014 Effects of fluctuating pressure gradients on boundary layer turbulence. J. Fluid Mech. 748, 36.CrossRefGoogle Scholar
de Kat, R. & Ganapathisubramani, R. B. 2013 Pressure from particle image velocimetry for convective flows: a Taylor's hypothesis approach. Meas. Sci. Technol. 24 (2), 024002.CrossRefGoogle Scholar
de Kat, R. & van Oudheusden, B. W. 2012 Instantaneous planar pressure determination from PIV in turbulent flow. Exp. Fluids 52 (5), 1089–1106.CrossRefGoogle Scholar
Kenney, J. F. & Keeping, E. S. 1962 The median, relation between mean, median and mode, relative merits of mean, median and mode. In Mathematics of Statistics, 3rd edn, vol. pt. 1. Van Nostrand.Google Scholar
Kern, S. & Koumoutsakos, P. 2006 Simulations of optimized anguilliform swimming. J. Expl Biol. 209 (24), 4841–4857.CrossRefGoogle ScholarPubMed
Khodarahmi, I., Shakeri, M., Sharp, M. & Amini, A. 2010 Using PIV to determine relative pressures in a stenotic phantom under steady flow based on the pressure-poisson equation. In Conference proceedings: …Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pp. 2594–2597.Google Scholar
Kim, D. & Gharib, M. 2010 Experimental study of three-dimensional vortex structures in translating and rotating plates. Exp. Fluids 49, 329–3390.CrossRefGoogle Scholar
Kobashi, Y. & Hayakawa, M. 1980 The transition mechanism of an oscillating boundary layer. In Laminar-Turbulent Transition (ed. R. Eppler & H. Fasel), pp. 102–109. Springer.CrossRefGoogle Scholar
Kottelat, M. 2017 Three new species of loaches of the genus Schistura from the Nam Ngiep drainage, central Laos (Teleostei: Nemacheilidae). Raffles Bull. Zool. 65, 691–706.Google Scholar
Kunze, S. & Brücker, C. 2011 Flow control over an undulating membrane. Exp. Fluids 50 (3), 747–759.CrossRefGoogle Scholar
Lai, W., Pan, G., Menon, R., Troolin, D., Castaño-Graff, E., Gharib, M. & Pereira, F. J. A. 2008 Volumetric three-component velocimetry: a new tool for 3D flow measurement. In 14th International Symposium on Applications of Laser Techniques to Fluid Mechanics.Google Scholar
Lauder, G. V. 1989 Caudal fin locomotion in ray-finned fishes: historical and functional analyses. Integr. Compar. Biol. 29 (1), 85–102.Google Scholar
Lauder, G. V. 2000 Function of the caudal fin during locomotion in fishes: kinematics, flow visualization, and evolutionary patterns. Am. Zool. 40 (1), 101–122.Google Scholar
Lauder, G. V. 2006 Locomotion. In The Physiology of Fishes (ed. D. H. Evans & J. B. Claiborne), pp. 3–46. CRC.Google Scholar
Lauder, G. V. 2015 Flexible fins and fin rays as key transformations in ray-finned fishes. In Great Transformations in Vertebrate Evolution, chap. 2. University of Chicago Press.Google Scholar
Lauder, G. V., Anderson, E., Tangorra, J. & Madden, P. 2007 Fish biorobotics: kinematics and hydrodynamics of self-propulsion. J. Expl Biol. 210, 2767–2780.CrossRefGoogle ScholarPubMed
Lauder, G. V. & Liem, K. F. 1983 The evolution and Interrelationships of the Actinopterygian Fishes. Bulletin of the Museum of Comparative Zoology at Harvard College.Google Scholar
Lauder, G. V., Madden, P., Hunter, I., Tangorra, J., Davidson, N., Proctor, L., Mittal, R., Dong, H. & Bozkurttas, M. 2005 Design and performance of a fish fin-like propulsor for AUVs. In 14th International Symposium on Unmanned Untethered Submersible Technology, Durham, NH.Google Scholar
Lauder, G. V. & Madden, P. G. A. 2007 Fish locomotion: kinematics and hydrodynamics of flexible foil-like fins. Exp. Fluids 43, 641–653.CrossRefGoogle Scholar
Lentink, D. 2008 Exploring the biofluiddynamics of swimming and flight. PhD thesis, Wageningen University.Google Scholar
Link, O., Sanhueza, C., Arriagada, P., Brevis, W., Laborde, A., González, A., Wilkes, M. & Habit, E. 2017 The fish Strouhal number as a criterion for hydraulic fishway design. Ecol. Engng 103, 118–126.CrossRefGoogle Scholar
Liu, G., Ren, Y., Dong, H., Akanyeti, O., Liao, J. & Lauder, G. V. 2017 Computational analysis of vortex dynamics and performance enhancement due to body–fin and fin–fin interactions in fish-like locomotion. J. Fluid Mech. 829, 65–88.CrossRefGoogle Scholar
Liu, X. & Katz, J. 2006 Instantaneous pressure and material acceleration measurements using a four-exposure PIV system. Exp. Fluids 41, 227–240.CrossRefGoogle Scholar
Lorenzoni, V., Tuinstra, M., Moore, P. & Scarano, F. 2009 Aeroacoustic Analysis of a Rod-Airfoil Flow by Means of Time-Resolved PIV. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Low, K. 2007 Design, development and locomotion control of bio-fish robot with undulating anal fins. Intl J. Robot. Autom. 22, 88–99.Google Scholar
Low, K. H. & Willy, A. 2006 Biomimetic motion planning of an undulating robotic fish fin. J. Vib. Control 12, 1337–1359.CrossRefGoogle Scholar
Lucas, K. N., Dabiri, J. O. & Lauder, G. V. 2017 A pressure-based force and torque prediction technique for the study of fish-like swimming. PLoS ONE 12, e0189225.CrossRefGoogle Scholar
Lucas, K., Thornycroft, P., Gemmell, B., Colin, S., Costello, J. & Lauder, G. 2015 Effects of non-uniform stiffness on the swimming performance of a passively-flexing, fish-like foil model. Bioinspir. Biomim. 10, doi:10.1088/1748-3190/10/5/056019.CrossRefGoogle ScholarPubMed
Maas, H. G., Gruen, A. & Papantoniou, D. 1993 Particle tracking velocimetry in three-dimensional flows. Exp. Fluids 15 (2), 133–146.CrossRefGoogle Scholar
Marais, C., Thiria, B., Wesfreid, J. & Godoy-Diana, R. 2012 Stabilizing effect of flexibility in the wake of a flapping foil. J. Fluid Mech. 710, 659–669.CrossRefGoogle Scholar
McClure, J. & Yarusevych, S. 2017 Optimization of planar PIV-based pressure estimates in laminar and turbulent wakes. Exp. Fluids 58, 62.CrossRefGoogle Scholar
McHenry, M. J. & Lauder, G. V. 2005 The mechanical scaling of coasting in zebrafish (Danio rerio). J. Expl Biol. 208 (12), 2289–2301.CrossRefGoogle Scholar
McNeill, A. R. 1974 Functional Design in Fishes. Hutchinson.Google Scholar
Mittal, R., Dong, H., Bozkurttas, M., Lauder, G. V. & Madden, P. 2006 Locomotion with flexible propulsors: II. Computational modeling of pectoral fin swimming in sunfish. Bioinspir. Biomim. 1 (4), S35–S41.CrossRefGoogle ScholarPubMed
Muir, R. E., Arredondo-Galeana, A. & Viola, I. M. 2017 The leading-edge vortex of swift wing-shaped delta wings. R. Soc. Open Sci. 4, 170077.CrossRefGoogle Scholar
Müller, U. K., van den Boogaart, J. G. M. & van Leeuwen, J. L. 2008 Flow patterns of larval fish: undulatory swimming in the intermediate flow regime. J. Expl Biol. 211 (2), 196–205.CrossRefGoogle ScholarPubMed
Müller, U. K., Smit, J., Stamhuis, E. J., Videler, J. J. 2001 How the body contributes to the wake in undulatory fish swimming: flow fields of a swimming eel (Anguilla anguilla). J. Expl Biol. 204, 2751–62.Google Scholar
Müller, U. K., Stamhuis, E. J. & Videler, J. J. 2000 Hydrodynamics of unsteady fish swimming and the effects of body size: comparing the flow fields of fish larvae and adults. J. Expl Biol. 203, 193–206.Google ScholarPubMed
Müller, U. K., Van Den Heuvel, B., Stamhuis, E. J. & Videler, J. J. 1997 Fish foot prints: morphology and energetics of the wake behind a continuously swimming mullet (Chelon labrosus Risso). J. Expl Biol. 200, 2893–906.Google Scholar
Müller, U. K. & Van Leeuwen, J. L. 2006 Undulatory fish swimming: from muscles to flow. Fish Fish. 7, 84–103.CrossRefGoogle Scholar
Murai, Y., Nakada, T., Suzuki, T. & Yamamoto, F. 2007 Particle tracking velocimetry applied to estimate the pressure field around a Savonius turbine. Meas. Sci. Technol. 18, 2491.CrossRefGoogle Scholar
Mwaffo, V., Zhang, P., Romero Cruz, S. & Porfiri, M. 2017 Zebrafish swimming in the flow: a particle image velocimetry study. PeerJ 5, e4041.CrossRefGoogle ScholarPubMed
Naruse, K., Tanaka, M. & Takeda, H. 2011 Medaka: A Model for Organogenesis, Human Disease, and Evolution. Springer.CrossRefGoogle Scholar
Nauen, J. C. & Lauder, G. V. 2002 a Hydrodynamics of caudal fin locomotion by chub mackerel, Scomber Japonicus (Scombridae). J. Expl Biol. 205 (12), 1709–1724.Google Scholar
Nauen, J. C. & Lauder, G. V. 2002 b Quantification of the wake of rainbow trout (Oncorhynchus mykiss) using three-dimensional stereoscopic digital particle image velocimetry. J. Expl Biol. 205 (21), 3271–3279.Google ScholarPubMed
Obremski, H. J. & Fejer, A. A. 1967 Transition in oscillating boundary layer flows. J. Fluid Mech. 29 (1), 93–111.CrossRefGoogle Scholar
Offen, N., Blum, N., Meyer, A. & Begemann, G. 2008 Fgfr1 signalling in the development of a sexually selected trait in vertebrates, the sword of swordtail fish. BMC Develop. Biol. 8, 98.CrossRefGoogle ScholarPubMed
van Oudheusden, B. W. 2008 Principles and application of velocimetry-based planar pressure imaging in compressible flows with shocks. Exp. Fluids 45 (4), 657–674.CrossRefGoogle Scholar
van Oudheusden, B. W. 2013 PIV-based pressure measurement. Meas. Sci. Technol. 24 (3), 032001.CrossRefGoogle Scholar
van Oudheusden, B. W., Scarano, F. & Casimiri, E. W. F. 2006 Non-intrusive load characterization of an airfoil using PIV. Exp. Fluids 40 (6), 988–992.CrossRefGoogle Scholar
van Oudheusden, B. W., Scarano, F., Roosenboom, E. W. M., Casimiri, E. W. F. & Souverein, L. J. 2007 Evaluation of integral forces and pressure fields from planar velocimetry data for incompressible and compressible flows. Exp. Fluids 43 (2), 153–162.CrossRefGoogle Scholar
Palstra, A. P., Tudorache, C., Rovira, M., Brittijn, S. A., Burgerhout, E., van den Thillart, G. E. E. J. M., Spaink, H. P. & Planas, J. V. 2010 Establishing zebrafish as a novel exercise model: swimming economy, swimming-enhanced growth and muscle growth marker gene expression. PLoS ONE 5 (12), e14483.CrossRefGoogle ScholarPubMed
Panciroli, R. & Porfiri, M. 2013 Evaluation of the pressure field on a rigid body entering a quiescent fluid through particle image velocimetry. Exp. Fluids 54 (12), 1630.CrossRefGoogle Scholar
Parichy, D. M., Elizondo, M. R., Mills, M., Gordon, T. N. & Engeszer, R. E. 2009 Normal table of post-embryonic zebrafish development: staging by externally visible anatomy of the living fish. Develop. Dyn. 238, 2975–3015.CrossRefGoogle Scholar
Pereira, F. J. A., Stüer, H., Graff, E. C. & Gharib, M. 2006 Two-frame 3D particle tracking. Meas. Sci. Technol. 17, 1680–1692.CrossRefGoogle Scholar
Plongsesthee, R., Beamish, F. & Page, L. 2012 Sexual dimorphism in species of Schistura (Teleostei: Nemacheilidae) from the Mae Khlong basin and peninsular Thailand. Zootaxa 3586, 353–358.CrossRefGoogle Scholar
Prandtl, L. 1952 Essentials of Fluid Dynamics: With Applications to Hydraulics Aeronautics, Meteorology, and Other Subjects. Hafner.Google Scholar
Puri, S. 2018 Approaching zebrafish (Danio rerio) caudal fin regeneration from a biomechanical perspective. PhD thesis, University of Zurich.Google Scholar
Puri, S., Aegerter-Wilmsen, T., Jaźwińska, A. & Aegerter, C. M. 2018 In vivo quantification of mechanical properties of caudal fins in adult zebrafish. J. Expl Biol. 221 (4), jeb171777.CrossRefGoogle ScholarPubMed
Qing Ping, W., Wang, S., Dong, X., Shang, L. J. & Tan, M. 2013 Design and kinetic analysis of a biomimetic underwater vehicle with two undulating long-fins. Acta Automat. Sinica 39 (8), 1330–1338.CrossRefGoogle Scholar
Quinn, D., Lauder, G. V. & Smits, A. 2014 Scaling the propulsive performance of heaving flexible panels. J. Fluid Mech. 738, 250–267.CrossRefGoogle Scholar
Quinn, D., Lauder, G. V. & Smits, A. 2015 Maximizing the efficiency of a flexible propulsor using experimental optimization. J. Fluid Mech. 767, 430–448.CrossRefGoogle Scholar
Raffel, M., Willert, C. E., Wereley, S. & Kompenhans, J. 1998 Particle Image Velocimetry: A Practical Guide. Springer.CrossRefGoogle Scholar
Ragni, D., van Oudheusden, B. W. & Scarano, F. 2012 3D pressure imaging of an aircraft propeller blade-tip flow by phase-locked stereoscopic PIV. ACM J. Expl Algorithms 52, 463–477.Google Scholar
Ren, Z., Hu, K., Wang, T. & Wen, L. 2016 a Investigation of fish caudal fin locomotion using a bio-inspired robotic model. Intl J. Adv. Robot. Syst. 13 (3), 87.CrossRefGoogle Scholar
Ren, Z., Yang, X., Wang, T. & Wen, L. 2016 b Hydrodynamics of a robotic fish tail: effects of the caudal peduncle, fin ray motions and the flow speed. Bioinspir. Biomim. 11, 016008.CrossRefGoogle ScholarPubMed
Rosic, M., Thornycroft, P., Feilich, K., Lucas, K. & Lauder, G. V. 2017 Performance variation due to stiffness in a tuna-inspired flexible foil model. Bioinspir. Biomim. 12, 016011.CrossRefGoogle Scholar
Sambilay, V. C. Jr. 2005 Interrelationships between swimming speed, caudal fin aspect ratio and body length of fishes. Fishbyte 8, 16–20.Google Scholar
Shelton, R. M., Thornycroft, P. J. M. & Lauder, G. V. 2014 Undulatory locomotion of flexible foils as biomimetic models for understanding fish propulsion. J. Expl Biol. 217 (12), 2110–2120.CrossRefGoogle ScholarPubMed
Shinde, S. & Arakeri, J. H. 2014 Flexibility in flapping foil suppresses meandering of induced jet in absence of free stream. J. Fluid Mech. 757, 231–250.CrossRefGoogle Scholar
Stamhuis, E. & Videler, J. 1995 Quantitative flow analysis around aquatic animals using laser sheet particle image velocimetry. J. Expl Biol. 198 (2), 283–294.Google ScholarPubMed
Tangorra, J. L., Davidson, S. N., Hunter, I. W., Madden, P. G. A., Lauder, G. V., Dong, H., Bozkurttas, M. & Mittal, R. 2007 The development of a biologically inspired propulsor for unmanned underwater vehicles. IEEE J. Ocean. Engng 32 (3), 533–550.CrossRefGoogle Scholar
Tangorra, J. L., Lauder, G. V., Hunter, I. W., Mittal, R., Madden, P. G. A. & Bozkurttas, M. 2010 The effect of fin ray flexural rigidity on the propulsive forces generated by a biorobotic fish pectoral fin. J. Expl Biol. 213 (23), 4043–4054.CrossRefGoogle ScholarPubMed
Taylor, G. K., Nudds, R. L. & Thomas, A. L. R. 2003 Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency. Nature 425 (6959), 707–711.CrossRefGoogle Scholar
Triantafyllou, M., Techet, A. & Hover, F. 2004 Review of experimental work in biomimetic foils. IEEE J. Ocean. Engng 29, 585–594.CrossRefGoogle Scholar
Triantafyllou, M., Triantafyllou, G. & Yue, D. K. P. 2000 Hydrodynamics of fishlike swimming. ARFM 32, 33–53.Google Scholar
Tronchin, T., David, L. & Farcy, A. 2015 Loads and pressure evaluation of the flow around a flapping wing from instantaneous 3D velocity measurements. Exp. Fluids 56 (1), 7.CrossRefGoogle Scholar
Tytell, E. D. 2006 Median fin function in bluegill sunfish lepomis macrochirus: streamwise vortex structure during steady swimming. J. Expl Biol. 209 (8), 1516–1534.CrossRefGoogle ScholarPubMed
Tytell, E. D., Standen, E. M. & Lauder, G. V. 2008 Escaping flatland: three-dimensional kinematics and hydrodynamics of median fins in fishes. J. Expl Biol. 211 (2), 187–195.CrossRefGoogle ScholarPubMed
Van Leeuwen, J. L., Voesenek, C. & Müller, U. 2015 How body torque and Strouhal number change with swimming speed and developmental stage in larval zebrafish. J. R. Soc. Interface 12, 20150479.CrossRefGoogle ScholarPubMed
Videler, J. 1975 On the interrelationships between morphology and movement in the tail of the cichlid fish Tilapia nilotica (L.). Neth. J. Zool. 25, 143–194.CrossRefGoogle Scholar
Violato, D., Moore, P. & Scarano, F. 2011 Lagrangian and Eulerian pressure field evaluation of rod-airfoil flow from time-resolved tomographic PIV. Exp. Fluids 50 (4), 1057–1070.CrossRefGoogle Scholar
Vogel, S. 1994 Life in Moving Fluids. Princeton University Press.Google Scholar
Wang, Z., Gao, Q., Wei, R. & Wang, J. 2017 Error propagation in the procedure of pressure reconstruction based on PIV data. J. Phys.: Conf. Ser. 822, 012055.Google Scholar
Wardle, C. S. 1975 Limit of fish swimming speed. Nature 255, 725–727.CrossRefGoogle ScholarPubMed
Webb, P. W. 1975 Hydrodynamics and Energetics of Fish Propulsion. Department of the Environment Fisheries and Marine Service.Google Scholar
Weerden, J., Reid, D. & Hemelrijk, C. 2013 A meta-analysis of steady undulatory swimming. Fish Fish. 15, 397–409.CrossRefGoogle Scholar
Weihs, D. 1989 Design features and mechanics of axial locomotion in fish. Am. Zool. 29 (1), 151–160.CrossRefGoogle Scholar
Whitaker, S. 1968 Introduction Fluid Mechanics. Prentice-Hall.Google Scholar
Windsor, S. P. 2008 Hydrodynamic imaging by blind Mexican cave fish. PhD thesis, University of Auckland.CrossRefGoogle Scholar
Xiong, G. & Lauder, G. V. 2014 Center of mass motion in swimming fish: effects of speed and locomotor mode during undulatory propulsion. Zoology 117 (4), 269–281.CrossRefGoogle ScholarPubMed
Yates, G. T. 1983 Hydrodynamics of body and caudal fin propulsion. In Fish Biomechanics, pp. 177–213. Praeger.Google Scholar
Zhou, C. & Low, K. H. 2012 Design and locomotion control of a biomimetic underwater vehicle with fin propulsion. IEEE-ASME Trans. Mechatron. 17, 25–35.CrossRefGoogle Scholar
Zhu, R., Wang, J., Lewis, G., Zhu, J., Dong, H., Bart-Smith, H., Wainwright, D. & Lauder, G. V. 2017 Propulsive performance of pitching panels with bio-inspired passive directional flexibility. AIAA Paper 2017-3980.CrossRefGoogle Scholar