Metachronal rowing provides robust propulsive performance across four orders of magnitude variation in Reynolds number

Abstract

Metachronal rowing of multiple appendages is a swimming strategy used by numerous organisms across various taxa, with body sizes ranging of the orders of [Formula: see text] to [Formula: see text] m. This corresponds to a huge variation in fluid flow regimes, characterized by paddle-scale Reynolds numbers ([Formula: see text]) ranging from the orders of [Formula: see text] (viscosity dominated) to [Formula: see text] (inertially dominated). Though the rhythmic stroking of the paddles is conserved across species and developmental stages, the hydrodynamic scalability of metachronal rowing has not been examined across this broad [Formula: see text] range. Using a self-propelled metachronal paddling robot, we examine swimming performance changes across four orders of magnitude variation in [Formula: see text] most relevant to crustaceans ([Formula: see text] to [Formula: see text]). We found that wake Strouhal number ([Formula: see text]), which characterizes momentum transfer from paddles to the wake, was unchanged for [Formula: see text] ([Formula: see text]). This is within the reported range of Strouhal numbers of various flying and swimming animals. Peak dimensionless circulation of paddle tip vortices increased linearly with stroke kinematics but was mostly unaffected by fluid viscosity. These findings show that the swimming performance of metachronal rowing is conserved across widely varying flow regimes, with dimensionless swimming speed scaling linearly with [Formula: see text] across the entire tested range.