Hydrodynamics of metachronal paddling: effects of varying Reynolds number and phase lag

Abstract

Negatively buoyant freely swimming crustaceans such as krill must generate downward momentum in order to maintain their position in the water column. These animals use a drag-based propulsion strategy, where pairs of closely spaced swimming limbs are oscillated rhythmically from the tail to head. Each pair is oscillated with a phase delay relative to the neighbouring pair, resulting in a metachronal wave travelling in the direction of animal motion. It remains unclear how oscillations of limbs in the horizontal plane can generate vertical momentum. Using particle image velocimetry measurements on a robotic model, we observed that metachronal paddling with non-zero phase lag created geometries of adjacent paddles that promote the formation of counter-rotating vortices. The interaction of these vortices resulted in generating large-scale angled downward jets. Increasing phase lag resulted in more vertical orientation of the jet, and phase lags in the range used by Antarctic krill produced the most total momentum. Synchronous paddling produced lower total momentum when compared with metachronal paddling. Lowering Reynolds number by an order of magnitude below the range of adult krill (250–1000) showed diminished downward propagation of the jet and lower vertical momentum. Our findings show that metachronal paddling is capable of producing flows that can generate both lift (vertical) and thrust (horizontal) forces needed for fast forward swimming and hovering.

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

“…Reynolds number results in the wake travelling farther downstream [32], consistent with the observation that the wake of E. superba can be detected several body lengths farther downstream than the wake of smaller Euphausia pacifica [25]. Assumptions inherent in numerical models have resulted in contradictory findings.…”

“…Albeit several studies of metachronal propulsion have been performed in freely-swimming crustaceans [4,19,21] and using numerical [2,[33][34][35] and robotic models [32,36], the effects of varying individual stroke kinematic parameters on free-swimming performance are unclear. We examined free-swimming performance as a function of inter-pleopod phase delay ( ) using a selfpropelled biomimetic krill robot.…”

“…As changes in E. superba gait kinematics involve coupled changes to two or more stroke kinematic parameters, alternative 79 approaches are necessary to identify functional roles of individual kinematic parameters. In this 80 regard, robotic [32] and numerical [2,[33][34][35][36] models can be useful to ascertain relative importance of morphological and kinematic parameters. Such studies can improve our understanding of organismenvironmental interactions in terms of what factors (morphological, kinematics) render a particular species well-suited to their specific environmental niches.…”

“…Numerical studies [2,34] have shown metachronal motion to enhance thrust, while an experimental study showed that metachrony can contribute to lift [32]. Additionally, increasing…”

Metachronal Swimming with Rigid Arms near Boundaries

“…The metachronal wave typically travels along the body of the swimmer in the direction of locomotion [4,6,11]. The swimming performance depends on numerous factors, which include the shape, amplitude, phase, and number of oscillating appendages [4,10,12,13].…”