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 10-5 to 10-1 m. This corresponds to a huge variation in fluid flow regimes, characterized by paddle-scale Reynolds numbers (ReL) ranging from the orders of ReL∼10-2 (viscosity dominated) to ReL∼105 (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 ReL range. Using a self-propelled metachronal paddling robot, we examine swimming performance changes across four orders of magnitude variation in ReL most relevant to crustaceans (101 to 104). We found that wake Strouhal number (Stw), which characterizes momentum transfer from paddles to the wake, was unchanged for ReL>42 (Stw≈0.26). 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 ReL across the entire tested range.