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Published February 15, 2007 | Published
Journal Article Open

Non-invasive measurement of instantaneous forces during aquatic locomotion: a case study of the bluegill sunfish pectoral fin


Swimming and flying animals generate unsteady locomotive forces by delivering net momentum into the fluid wake. Hence, swimming and flying forces can be quantified by measuring the momentum of animal wakes. A recently developed model provides an approach to empirically deduce swimming and flying forces based on the measurement of velocity and vortex added-mass in the animal wake. The model is contingent on the identification of the vortex boundary in the wake. This paper demonstrates the application of that method to a case study quantifying the instantaneous locomotive forces generated by the pectoral fins of the bluegill sunfish (Lepomis macrochirus Rafinesque), measured using digital particle image velocimetry (DPIV). The finite-time Lyapunov exponent (FTLE) field calculated from the DPIV data was used to determine the wake vortex boundary, according to recently developed fluid dynamics theory. Momentum of the vortex wake and its added-mass were determined and the corresponding instantaneous locomotive forces were quantified at discrete time points during the fin stroke. The instantaneous forces estimated in this study agree in magnitude with the time-averaged forces quantified for the pectoral fin of the same species swimming in similar conditions and are consistent with the observed global motion of the animals. A key result of this study is its suggestion that the dynamical effect of the vortex wake on locomotion is to replace the real animal fin with an `effective appendage', whose geometry is dictated by the FTLE field and whose interaction with the surrounding fluid is wholly dictated by inviscid concepts from potential flow theory. Benefits and limitations of this new framework for non-invasive instantaneous force measurement are discussed, and its application to comparative biomechanics and engineering studies is suggested.

Additional Information

Published by The Company of Biologists 2007. Accepted 12 December 2006. First published online January 31, 2007. The authors thank Shawn Shadden, Jerry Marsden and Parviz Moin for discussions of the LCS theory. This work was supported by NSF grant OCE0623475 to J.O.D.; an ONR-MURI Grant N00014-03-1-0897 on fish pectoral fin function, monitored by Dr Thomas McKenna and initiated by Dr Promode Bandyopadhyay; and NSF grant IBN0316675 to G.V.L.

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