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Hydrodynamically coupled oscillators

Published online by Cambridge University Press:  19 April 2011

R. TIRON ,
E. KANSO  and
P. K. NEWTON
R. TIRON
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
E. KANSO*
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
P. K. NEWTON
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA
*
†Email address for correspondence: kanso@usc.edu
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Abstract

A submerged spring–mass ring is analysed as a simple model for the way in which an underwater swimmer couples its body deformations to the surrounding fluid in order to accomplish locomotion. We adopt an inviscid, incompressible, irrotational assumption for the surrounding fluid and analyse the coupling response to various modes of excitation of the ring configuration. Due to the added mass effect, the surrounding fluid provides an environment which effectively couples the ‘normal modes’ of oscillation of the ring, leading to nonlinear trajectories if the ring is free to accelerate based on the effective forces the oscillations induce. Through a series of examples, we demonstrate various features that the model supports, including the locomotion on curved paths as a result of energy and angular momentum exchange with the surrounding fluid.

JFM classification

Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Biological Fluid Dynamics: Swimming/flying
Type
Papers
Information
Journal of Fluid Mechanics , Volume 677 , 25 June 2011 , pp. 589 - 606
Copyright
Copyright © Cambridge University Press 2011

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References

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