Abstract
The passive locomotion of a body placed in a thrust wake is examined. This work is motivated by a common belief that live and inanimate objects may extract energy from unsteady flows for locomotory advantages. We propose idealized wake models using periodically-generated point vortices to emulate shedding of vortices from an un-modeled moving (thrust) object. We investigate the two-way coupled dynamics of a submerged rigid body with such thrust wakes. In particular, we seek and obtain periodic trajectories where a circular body ‘swims’ passively against the flow of a thrust wake by extracting energy from the ambient vortices. These periodic trajectories are unstable, as indicated by the associated Floquet multipliers. The instabilities are particularly strong for elliptic bodies where rotational effects are at play.
AMS(MOS) subject classifications. 76Z10s, 76B47, 37N25
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References
Alben S (2010) Passive and active bodies in vortex-street wakes. J Fluid Mech 642:95–125
Aref H, Rott N, Thomann H (1992) Gröblis solution of the three-vortex problem. Annu Rev Fluid Mech 24:1–20
Beal DN, Hover FS, Triantafyllou MS, Liao JC, Lauder GV (2006) Passive propulsion in vortex wakes. J Fluid Mech 549:385–402
Bose N, Lien J (1990) Energy absorption from ocean waves: a free ride on cetaceans. Proc R Soc Lond 240:591–605
Borisov AV, Mamaev IS, Ramodanov SM (2007) Dynamic interaction of point vortices and a two-dimensional cylinder. J Math Phys 48:1–9
Hayes WD (1953) Wave riding of dolphins. Nature 172:1060
Eldredge JD, Pisani D (2008) Passive locomotion of a simple articulated fish-like system in the wake of an obstacle. J Fluid Mech 607:279–288
Fausch KD (1993) Experimental analysis of microhabitat selection by juvenile steel head (Oncorhynchus mykiss) and coho salmon (O. kisutch) in a British Columbia stream. Can J Fish Aquat Sci 50:1198–1207
Jing F, Kanso E (2012) Effects of body elasticity on the stability of underwater motion, J Fluid Mech 690:461–473
Kanso E, Oskouei BG (2008) Stability of a coupled body-vortex system. J Fluid Mech 800:77–94
Liao JC, Beal DN, Lauder GV, Triantafyllou MS (2003) Fish exploiting vortices decrease muscle activity. Science 302:1566–1569
Oskouei BG (2011) Body-vortex dynamics: application to aquatic locomotion. Ph.D. dissertation, University of Southern California
Roenby J, Aref H (2010) Chaos in body-vortex interactions. Proc R Soc Lond A 466:1871–1891
Shashikanth BN, Marsden JE, Burdick JW, Kelly SD (2002) The Hamiltonian structure of a 2D rigid circular cylinder interacting dynamically with N point vortices. Phys Fluid 14:1214–1227
Webb PW (1998) Entrainment by river chub Nocomis micropogon and smallmouth bass micropterus dolomieu on cylinders. J Exp Biol 201:2403–2412
Wu TY, Chwang AT (1974) Extraction of flow energy by fish and birds in a wavy stream. Proceeding of the symposium on swimming and flying in nature, California Institute of Technology, Pasadena, pp 687–702
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Oskouei, B.G., Kanso, E. (2012). Stability of Passive Locomotion in Periodically-Generated Vortex Wakes. In: Childress, S., Hosoi, A., Schultz, W., Wang, J. (eds) Natural Locomotion in Fluids and on Surfaces. The IMA Volumes in Mathematics and its Applications, vol 155. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3997-4_20
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DOI: https://doi.org/10.1007/978-1-4614-3997-4_20
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