Rapidly yawing spheroids in viscous shear flow: Emergent loss of symmetry

Abstract

We investigate the emergent dynamics of a rapidly yawing spheroidal swimmer interacting with a viscous shear flow. We show that the rapid yawing generates non-axisymmetric emergent effects, with the active swimmer behaving as an effective passive particle with two orthogonal planes of symmetry. The shape of the equivalent effective particle is different to the average shape of the active particle. Moreover, despite having two planes of symmetry, the equivalent passive particle is not an ellipsoid in general, except for specific scenarios in which the effective shape is a spheroid. We use a multiple scales analysis for systems to derive the emergent swimmer behaviour, which requires solving a nonautonomous nonlinear 3D dynamical system, and we validate our analysis via comparison to numerical simulations.