Metachronal swimming consists of the sequential stroking of multiple appendages or cilia, resulting in a wave of appendage motion traveling along the body. Further, metachronal swimming spans the viscous to inertial regimes as it is used across seven orders of magnitude of Reynolds numbers ${\mathrm{Re}}_b$, where ${\mathrm{Re}}_b=VL/\nu$, and $V, L$, and $\nu$ are the characteristic swimming speed, body length, and fluid kinematic viscosity, respectively. Through analysis of morphological and kinematics data collected from the literature on a wide variety of metachronally swimming organisms, we examine how these factors affect swimming performance across ${\mathrm{Re}}_b$. Further, we find a strong relationship among the kinematics parameters, swimming speed, and fluid viscosity. This power law relationship, ${\mathrm{Re}}_b\sim Sw$, where $Sw=\omega AL/\nu$ is the Swimming number ($\omega$: average angular appendage tip speed, $A$: appendage tip excursion), is maintained for all flow regimes, explains why metachronal swimming is a successful locomotion mode at low Reynolds numbers, and may prove useful in designing bio-inspired robots. We also find that the Strouhal number $St=fA/V$, where $f$ is beat frequency, is relatively constant across a wide range of ${\mathrm{Re}}_b$ but suggest that $Sw$ better describes the underlying hydrodynamics of metachronal swimming.

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• Biological fluid dynamics
• Swimming