Wave-riding and wave-passing by ducklings in formation swimming

Abstract

It has been commonly observed on open waters that ducklings/goslings follow their mothers in a highly organized formation. The questions arise: (1) why are they swimming in formation? (2) what is the best swimming formation? (3) how much energy can be preserved by each individual in formation swimming? To address these questions, we established a simplified mathematical and numerical model and calculated the wave drag on a group of waterfowl in a swimming formation. We observed two new and interesting findings: wave-riding and wave-passing. By riding the waves generated by a mother duck, a trailing duckling can obtain a significant wave-drag reduction. When a duckling swims at the ‘sweet point’ behind its mother, a destructive wave interference phenomenon occurs and the wave drag of the duckling turns positive, pushing the duckling forward. More interestingly, this wave-riding benefit could be sustained by the rest of the ducklings in a single-file line formation. Starting from the third one in a queue, the wave drag of individuals gradually tended towards zero, and a delicate dynamic equilibrium was achieved. Each individual under that equilibrium acted as a wave passer, passing the waves’ energy to its trailing one without any energy losses. Wave-riding and wave-passing are probably the principal reasons for the evolution of swimming formation by waterfowl. This study is the first to reveal the reasons why the formation movement of waterfowl can preserve individuals’ energy expenditure. Our calculations provide new insights into the mechanisms of formation swimming.

Gunwale bobbing

“…We demonstrate that certain combinations of pitching and heaving produce a positive thrust force; the canoe "surfs its own waves" (see also Ref. [5] which discusses wake-surfing ducklings). We balance this positive thrust against negative resistive forces due to wave and profile drag to find the steady cruising speed.…”

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“…Two groups of researchers—from China, Turkey, the UK, and the US—revealed why ducklings swim in a row behind their mother and won the physics prize. The mother duck generates a wave and the ducklings behind her ride along the wave and the benefit is passed on to each duckling in the row 56…”

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“…2021; Yuan et al. 2021). It can reduce the metabolic cost in birds and fish alike (Herskin & Steffensen 1998; Weimerskirch et al.…”

“…Living organisms often move as a group. Besides social interactions that drive such collective locomotion, fluid-dynamic coupling has been recognized as an important factor for formation and gait selection in groups of swimming and flying organisms (Herskin & Steffensen 1998;Weimerskirch et al 2001;Brumley et al 2014;Ashraf et al 2016;Li et al 2021;Yuan et al 2021). It can reduce the metabolic cost in birds and fish alike (Herskin & Steffensen 1998;Weimerskirch et al 2001).…”