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      Passive appendages generate drift through symmetry breaking

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          Abstract

          Plants and animals use plumes, barbs, tails, feathers, hairs and fins to aid locomotion. Many of these appendages are not actively controlled, instead they have to interact passively with the surrounding fluid to generate motion. Here, we use theory, experiments and numerical simulations to show that an object with a protrusion in a separated flow drifts sideways by exploiting a symmetry-breaking instability similar to the instability of an inverted pendulum. Our model explains why the straight position of an appendage in a fluid flow is unstable and how it stabilizes either to the left or right of the incoming flow direction. It is plausible that organisms with appendages in a separated flow use this newly discovered mechanism for locomotion; examples include the drift of plumed seeds without wind and the passive reorientation of motile animals.

          Abstract

          Passive mechanisms without energy input are the only way for non-motile organisms to disperse in fluids. Here, the authors use the analogue of the inverted pendulum motion upon gravity to explain the passive drift of a body with a protrusion to the sides of an incoming fluid stream.

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          Most cited references4

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          How animals move: an integrative view.

          Recent advances in integrative studies of locomotion have revealed several general principles. Energy storage and exchange mechanisms discovered in walking and running bipeds apply to multilegged locomotion and even to flying and swimming. Nonpropulsive lateral forces can be sizable, but they may benefit stability, maneuverability, or other criteria that become apparent in natural environments. Locomotor control systems combine rapid mechanical preflexes with multimodal sensory feedback and feedforward commands. Muscles have a surprising variety of functions in locomotion, serving as motors, brakes, springs, and struts. Integrative approaches reveal not only how each component within a locomotor system operates but how they function as a collective whole.
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            Fluid-flow-induced flutter of a flag.

            We give an explanation for the onset of fluid-flow-induced flutter in a flag. Our theory accounts for the various physical mechanisms at work: the finite length and the small but finite bending stiffness of the flag, the unsteadiness of the flow, the added mass effect, and vortex shedding from the trailing edge. Our analysis allows us to predict a critical speed for the onset of flapping as well as the frequency of flapping. We find that in a particular limit corresponding to a low-density fluid flowing over a soft high-density flag, the flapping instability is akin to a resonance between the mode of oscillation of a rigid pivoted airfoil in a flow and a hinged-free elastic plate vibrating in its lowest mode.
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              Spontaneous symmetry breaking of a hinged flapping filament generates lift.

              Elastic filamentous structures found on swimming and flying organisms are versatile in function, rendering their precise contribution to locomotion difficult to assess. We show in this Letter that a single passive filament hinged on the rear of a bluff body placed in a stream can generate a net lift force without increasing the mean drag force on the body. This is a consequence of spontaneous symmetry breaking in the filament's flapping dynamics. The phenomenon is related to a resonance between the frequency associated with the von Kármán vortex street developing behind the bluff body and the natural frequency of the free bending vibrations of the filament.
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                Author and article information

                Journal
                Nat Commun
                Nat Commun
                Nature Communications
                Nature Pub. Group
                2041-1723
                30 October 2014
                : 5
                : 5310
                Affiliations
                [1 ]Linné Flow Centre, KTH Royal Institute of Technology, Department of Mechanics , 10044 Stockholm, Sweden
                [2 ]Department of Mechanical and Aerospace Engineering, Princeton University , Princeton, New Jersey 08544, USA
                [3 ]Department of Chemical, Civil and Environmental Engineering (DICCA), University of Genova , 16145 Genova, Italy
                [4 ]INFN and CINFAI Consortium, Genova Section , 16146 Genova, Italy
                [5 ]Université de Bordeaux, Laboratoire Ondes et Matière d'Aquitaine (UMR 5798 CNRS), 351 cours de la Libération , 33405 Talence, France
                Author notes
                Article
                ncomms6310
                10.1038/ncomms6310
                4220513
                25354545
                72469d20-7d8f-429d-b54a-1bf8d5bf312c
                Copyright © 2014, Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.

                This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

                History
                : 24 February 2014
                : 18 September 2014
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