On the role of phase lag in multi-appendage metachronal swimming of euphausiids

Abstract

Metachronal paddling is a common method of drag-based aquatic propulsion, in which a series of swimming appendages are oscillated, with the motion of each appendage phase-shifted relative to the neighboring appendages. Ecologically and economically important euphausiid species such as Antarctic krill (Euphausia superba) swim constantly by stroking their paddling appendages (pleopods), with locomotion accounting for the bulk of their metabolic expenditure. They tailor their swimming gaits for behavioral and energetic needs by changing pleopod kinematics. The functional importance of inter-pleopod phase lag (ϕ) to metachronal swimming performance and wake structure is unknown. To examine this relation, we developed a geometrically and dynamically scaled robot ('krillbot') capable of self-propulsion. Krillbot pleopods were prescribed to mimic published kinematics of fast-forward swimming (FFW) and hovering (HOV) gaits ofE. superba, and the Reynolds number and Strouhal number of the krillbot matched well with those calculated for freely-swimmingE. superba. In addition to examining published kinematics with unevenϕbetween pleopod pairs, we modifiedE. superbakinematics to uniformly varyϕfrom 0% to 50% of the cycle. Swimming speed and thrust were largest for FFW withϕbetween 15%-25%, coincident withϕrange observed in FFW gait ofE. superba. In contrast to synchronous rowing (ϕ= 0%) where distances between hinged joints of adjacent pleopods were nearly constant throughout the cycle, metachronal rowing (ϕ> 0%) brought adjacent pleopods closer together and moved them farther apart. This factor minimized body position fluctuation and augmented metachronal swimming speed. Though swimming speed was lowest for HOV, a ventrally angled downward jet was generated that can assist with weight support during feeding. In summary, our findings show that inter-appendage phase lag can drastically alter both metachronal swimming speed and the large-scale wake structure.

Keywords: Metachronal Swimming; aquatic locomotion; krill swimming; metachronal paddling; rowing.