Hydrodynamic scaling of metachronal swimming

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 Reb, where Reb = 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 Reb. Further, we find a strong relationship among the kinematics parameters, swimming speed, and fluid viscosity. This power law relationship, Reb similar to S w , where S w = 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 Reb but suggest that S w better describes the underlying hydrodynamics of metachronal swimming.