Reynolds number scalability of metachronal paddling

Metachronal paddling is a form of drag-based locomotion that is used by numerous aquatic organisms of sizes varying on the order of 0.01 mm to 100 mm. The paddling rhythm remains similar despite a wide variation in appendage-based Reynolds number on the orders of 10^-2 to 10³. We examined the effect of varying Reynolds number on the metachronal paddling wake and swimming performance. We conducted time-resolved 2D-2C PIV measurements on a dynamically similar metachronal paddling robotic model. Stroke frequency was varied from 1.5 to 3 Hz, while fluid viscosity was varied from 1 to 800 cSt, to obtain Reynolds numbers ranging from 35 to 54,000. Changing the fluid viscosity was found to greatly affect the direction and structure of the wake, while changing the stroke frequency was found to affect cycle to cycle interactions in the wake. For a given viscosity, steady swimming speed was found to vary linearly with stroke frequency. At steady swimming, the ratio of thrust to drag coefficients was found to decrease slightly with increasing Reynolds number. The Strouhal number was found to remain nearly constant in the range of 50 < Re < 54,000, indicating that metachronal paddling is a robust strategy that can function across size, stroke frequency and viscosity scales.