Emergent rheotaxis of shape-changing swimmers in Poiseuille flow

A simple model for the motion of shape-changing swimmers in Poiseuille flow was recently proposed and numerically explored by Omori et al. ( J. Fluid Mech. , vol. 930, 2022, A30). These explorations hinted that a small number interacting mechanics can drive long-time behaviours this model, cast context well-studied alga Chlamydomonas its rheotactic such flows. Here, we explore analytically via multiple-scale asymptotic analysis, seeking to formally identify causal factors shape behaviour these flow. By capturing evolution Hamiltonian-like quantity, reveal origins long-term drift single swimmer-dependent constant, whose sign determines eventual swimmer. This constant captures nonlinear interaction between oscillatory speed effective hydrodynamic deforming swimmers, driving either towards or away from rheotaxis.