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We examine the motion of rigid, ellipsoidal swimmers subjected to a steady vortex flow in two dimensions. Numerical simulations of swimmers in a spatially periodic array of vortices reveal a range of possible behaviors, including trapping inside a single vortex and motility-induced diffusion across many vortices. While the trapping probability vanishes at a sufficiently high swimming speed, we find that it exhibits surprisingly large oscillations as this critical swimming speed is approached. Strikingly, at even higher swimming speeds, we find swimmers that swim perpendicular to their elongation direction can again become trapped. To explain this complex behavior, we investigate the underlying swimmer phase-space geometry. We identify the fixed points and periodic orbits of the swimmer equations of motion that regulate swimmer trapping inside a single vortex cell. For low to intermediate swimming speeds, we find that a stable periodic orbit surrounded by invariant tori forms a transport barrier to swimmers and can trap them inside individual vortices. For swimming speeds approaching the maximum fluid speed, we find instead that perpendicular swimmers can be trapped by asymptotically stable fixed points. A bifurcation analysis of the stable periodic orbit and the fixed points explains the complex and non-monotonic breakdown and reemergence of swimmer trapping as the swimmer speed and shape are varied.
We investigate the way in which oscillating dumb-bells, a simple microscopic model of apolar swimmers, move at low Reynolds number. In accordance with Purcells Scallop Theorem a single dumb-bell cannot swim because its stroke is reciprocal in time. H
Fish schools and bird flocks exhibit complex collective dynamics whose self-organization principles are largely unknown. The influence of hydrodynamics on such collectives has been relatively unexplored theoretically, in part due to the difficulty in
We investigate the stability of a one-parameter family of periodic solutions of the four-vortex problem known as `leapfrogging orbits. These solutions, which consist of two pairs of identical yet oppositely-signed vortices, were known to W. Grobli (1
A system of ferromagnetic particles trapped at a liquid-liquid interface and subjected to a set of magnetic fields (magnetocapillary swimmers) is studied numerically using a hybrid method combining the pseudopotential lattice Boltzmann method and the
Surface interactions provide a class of mechanisms which can be employed for propulsion of micro- and nanometer sized particles. We investigate the related efficiency of externally and self-propelled swimmers. A general scaling relation is derived sh