Dynamics, Geometry, and Stability of Low Reynolds Number Swimming Near a Wall

Yizhar Or, Richard M Murray
Physical Review Letters, 2008 (Submitted)

We study the dynamics of low Reynolds number swimming near a plane wall by using a simple theoretical swimmer model that accounts for far-field hydrodynamic interactions. We focus on steady motion parallel to the wall and derive conditions under which it is passively stable without sensing or feedback. We highlight the geometric structure of the swimming equation and particularly the relation between stability and reversing symmetry of the wall-swimmer dynamics. Furthermore, in the case of unstable parallel swimming, our numerical simulations reveal the existence of a stable periodic motion along the wall, associated with a degenerate Hopf bifurcation.

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