Swimming, flying, and diving behaviors from a unified\xa02D potential model

Sunghwan Jung

doi:10.1038/s41598-021-94829-7

Abstract

Animals swim in water, fly in air, or dive into water to find mates, chase prey, or escape from predators. Even though these locomotion modes are phenomenologically distinct, we can rationalize the underlying hydrodynamic forces using a unified fluid potential model. First, we review the previously known complex potential of a moving thin plate to describe circulation and pressure around the body. Then, the impact force in diving or thrust force in swimming and flying are evaluated from the potential flow model. For the impact force, we show that the slamming or impact force of various ellipsoid-shaped bodies of animals increases with animal weight, however, the impact pressure does not vary much. For fliers, birds and bats follow a linear correlation between thrust lift force and animal weight. For swimming animals, we present a scaling of swimming speed as a balance of thrust force with drag, which is verified with biological data. Under this framework, three distinct animal behaviors (i.e., swimming, flying, and diving) are similar in that a thin appendage displaces and pressurizes a fluid, but different in regards to the surroundings, being either fully immersed in a fluid or at a fluid interface.

Highlights

In nature, animals move in fluids with different locomotive modes: swimming, flying, jumping out of water, or diving into water
We reviewed the previously known potential model of a plate moving in a fluid using a complex potential and provided analogies to swimming, flying, and diving of animals
The calculated force was decoded into the impact force for diving animals at the free surface or the thrust force for swimming or flying animals immersed in a fluid

Summary

Introduction

Animals move in fluids with different locomotive modes: swimming, flying, jumping out of water, or diving into water. James Lighthill pioneered the small- or large-amplitude elongated body theory to understand the swimming speed through balancing the power generated by an animal with the rate of kinetic energy in a fluid[1,9] This slender body approximation quantifies the efficiency of locomotion for aquatic animals analytically, and has been widely used. Theodore Wu described animal locomotion using an inviscid potential flow[2,10], which is an extension of the previously known potential flow of a thin plate This calculation explains the pressure difference across a thin object while flapping, which is linked to the vortex generation and thrust force. These two studies are limited to swimming or flying animals while fully immersed in a fluid.

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