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

Abstract

<jats:title>Abstract</jats:title><jats:p>Metachronal paddling is a common method of drag-based biological 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 (<jats:italic>E. superba</jats:italic>) swim constantly in the pelagic zone by stroking their paddling appendages (pleopods), with locomotion accounting for the bulk of their metabolic expenditure. They tailor their metachronal swimming gaits for behavioral and energetic needs by changing pleopod kinematics. The functional importance of inter-pleopod phase lag (<jats:italic>ϕ</jats:italic>) 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 of <jats:italic>E. superba</jats:italic>, and the Reynolds number and Strouhal number of the krillbot matched well with those calculated for freely-swimming <jats:italic>E. superba</jats:italic>. In addition to examining published kinematics with uneven <jats:italic>ϕ</jats:italic> between pleopod pairs, we modified <jats:italic>E. superba</jats:italic> kinematics to uniformly vary <jats:italic>ϕ</jats:italic> from 0% to 50% of the cycle. Swimming speed and thrust were largest for FFW with <jats:italic>ϕ</jats:italic> between 15%-25%, coincident with <jats:italic>ϕ</jats:italic> range observed in FFW gait of <jats:italic>E. superba</jats:italic>. In contrast to synchronous rowing (<jats:italic>ϕ</jats:italic>=0%) where distances between hinged joints of adjacent pleopods were nearly constant throughout the cycle, metachronal rowing (<jats:italic>ϕ</jats:italic>&gt;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 and hydrodynamic signaling in schooling krill. In summary, our findings show that inter-appendage phase lag can drastically alter both metachronal swimming speed and the large-scale wake structure.</jats:p>