Hydrodynamic bound states of a low-Reynolds-number swimmer near a gap in a wall

Author:

CROWDY DARREN,SAMSON OPHIR

Abstract

The motion of an organism swimming at low Reynolds number near an infinite straight wall with a finite-length gap is studied theoretically within the framework of a two-dimensional model. The swimmer is modelled as a point singularity of the Stokes equations dependent on a single real parameter. A dynamical system governing the position and orientation of the model swimmer is derived in analytical form. The dynamical system is studied in detail and a bifurcation analysis performed. The analysis reveals,inter alia, the presence of stable equilibrium points in the gap region as well as Hopf bifurcations to periodic bound states. The reduced-model system also exhibits a global gluing bifurcation in which two symmetric periodic orbits merge at a saddle point into symmetric ‘figure-of-eight’ bound states having more complex spatiotemporal structure. The additional effect of a background shear is also studied and is found to introduce new types of bound state. The analysis allows us to make theoretical predictions as to the possible behaviour of a low-Reynolds-number swimmer near a gap in a wall. It offers insights into the use of gaps or orifices as possible control devices for such swimmers in confined environments.

Publisher

Cambridge University Press (CUP)

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

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