Hydrodynamically coupled oscillators

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.