On the diverse roles of fluid dynamic drag in animal swimming and flying

Abstract

Questions of energy dissipation or friction appear immediately when addressing the problem of a body moving in a fluid. For the most simple problems, involving a constant steady propulsive force on the body, a straightforward relation can be established balancing this driving force with a skin friction or form drag, depending on the Reynolds number and body geometry. This elementary relation closes the full dynamical problem and sets, for instance, average cruising velocity or energy cost. In the case of finite-sized and time-deformable bodies though, such as flapping flyers or undulatory swimmers, the comprehension of driving/dissipation interactions is not straightforward. The intrinsic unsteadiness of the flapping and deforming animal bodies complicates the usual application of classical fluid dynamic forces balance. One of the complications is because the shape of the body is indeed changing in time, accelerating and decelerating perpetually, but also because the role of drag (more specifically the role of the local drag) has two different facets, contributing at the same time to global dissipation and to driving forces. This causes situations where a strong drag is not necessarily equivalent to inefficient systems. A lot of living systems are precisely using strong sources of drag to optimize their performance. In addition to revisiting classical results under the light of recent research on these questions, we discuss in this review the crucial role of drag from another point of view that concerns the fluid-structure interaction problem of animal locomotion. We consider, in particular, the dynamic subtleties brought by the quadratic drag that resists transverse motions of a flexible body or appendage performing complex kinematics, such as the phase dynamics of a flexible flapping wing, the propagative nature of the bending wave in undulatory swimmers, or the surprising relevance of drag-based resistive thrust in inertial swimmers.

Functional performance of turtle humerus shape across an ecological adaptive landscape

“…Animals locomoting under water will experience drag on their bodies and limbs. The swimming efficiency of marine and semiaquatic turtles will be determined not only by their propulsive capacity, but also by how much drag they experience (Godoy‐Diana and Thiria ). Although propulsion is hard to determine from only morphometric measures, the drag coefficient is inversely proportional to the frontal area of an object (Nachtigall ; Godoy‐Diana and Thiria ).…”

“…The swimming efficiency of marine and semiaquatic turtles will be determined not only by their propulsive capacity, but also by how much drag they experience (Godoy‐Diana and Thiria ). Although propulsion is hard to determine from only morphometric measures, the drag coefficient is inversely proportional to the frontal area of an object (Nachtigall ; Godoy‐Diana and Thiria ). Drag is an important limiting factor for both lift and drag‐based swimming in turtles, and a broad frontal area of the limb will present a larger surface for drag during swimming—reducing locomotor efficiency.…”

“…Although it is reasonable that terrestrial turtle humeri are adapted for strength, stride length, and muscular mechanical advantage, it is somewhat counterintuitive that terrestrial turtles maintain a need for hydrodynamic efficiency, considering the rarity of swimming behaviors. Such a signal may be an artifact of having aquatic ancestors, or of imperfect characterization of shapefrontal area is certainly a factor in hydrodynamics (Nachtigall 1981;Godoy-Diana and Thiria 2018) but it also likely has multiple other functional correlates. Despite facing much greater forces on land (Young et al 2017b), the shapes of terrestrial turtle humeri are modeled as being less strong than marine turtle humeri.…”

Insect and insect-inspired aerodynamics: unsteadiness, structural mechanics and flight control

“…However, non-trivial mechanisms have been shown to govern the performance of flexible wings in terms of their aerodynamics. In particular, drag induces a phase lag between the leading and trailing edges of the wing that brings a beneficial effect in terms of aerodynamic force production [39,40]. …”

Exploring the functional meaning of head shape disparity in aquatic snakes

“…All considered species successfully capture aquatic prey despite the hydrodynamic constraints they face (Segall et al, 2019; Van Wassenbergh et al, 2010). As these constraints are related to head shape (Fish, 2004; Godoy-Diana & Thiria, 2018; Koehl, 1996; Polly et al, 2016), we expected the observed morphological disparity to have functionally converged (i.e. have the same hydrodynamic profile) which would indicate a many-to-one-mapping of form to function (Wainwright et al, 2005).…”