Dynamic mode decomposition of the metachronal paddling wake

Abstract

Metachronal paddling is a drag-based propulsion strategy observed in many aquatic arthropods in which a series of paddling appendages are stroked sequentially to form a traveling wave in the same direction as animal motion. Metachronal paddling’s relatively high force production makes these organisms highly agile, an attractive potential for bio-inspired autonomous underwater vehicles that is complicated by the lack of reduced order flow structure and dynamics models applicable to vehicle actuation and control design. This study uses particle image velocimetry to quantify the wake of a robot performing metachronal paddling. Then, dynamic mode decomposition is used to identify the frequency modes of the wake, which are used to reconstruct a reduced order model at Reynolds numbers of 32, 160, and 516. The results show that the kinetic energy in the metachronal paddling wake is well modeled using a superposition of the first 5 dynamic modes, and that there is typically little change in the reconstruction error when the reconstruction is performed with a higher number of dynamic modes. The low order paddling models identified using this method can be used to identify the physical mechanisms that differentiate metachronal paddling from synchronous paddling, and to develop control strategies to modulate these motions in bio-inspired autonomous underwater vehicles.