Hydrodynamic scaling of metachronal swimming

Metachronal swimming is a common form of locomotion in which organisms stroke multiple appendages sequentially. It is used by many aquatic organisms, including paramecia, copepods, ctenophores, and krill, and spans the viscous to inertial regimes across seven orders of magnitude of Reynolds numbers (Re). Through analysis of morphological and kinematics data collected from the literature, we find a strong power law relationship between Re and the Swimming Number Sw, which describes the appendage kinematics. This scaling law is maintained for all flow regimes, explains why metachronal swimming is successful at low Re, and may be useful in designing bio-inspired metachronally paddling robots.