The Swimming of Whales and a Discussion of Gray's Paradox

Scaling of oscillatory kinematics and Froude efficiency in baleen whales

High efficiency lunate-tail swimming with high-aspect-ratio lifting surfaces has evolved in many vertebrate lineages, from fish to cetaceans. Baleen whales (Mysticeti) are the largest swimming animals that exhibit this locomotor strategy, and present an ideal study system to examine how morphology and the kinematics of swimming scale to the largest body sizes. We used data from whale-borne inertial sensors coupled with morphometric measurements from aerial drones to calculate the hydrodynamic performance of oscillatory swimming in six baleen whale species ranging in body length from 5 to 25 m (fin whale, Balaenoptera physalus; Bryde's whale, Balaenoptera edeni; sei whale, Balaenoptera borealis; Antarctic minke whale, Balaenoptera bonaerensis; humpback whale, Megaptera novaeangliae; and blue whale, Balaenoptera musculus). We found that mass-specific thrust increased with both swimming speed and body size. Froude efficiency, defined as the ratio of useful power output to the rate of energy input ( Sloop, 1978), generally increased with swimming speed but decreased on average with increasing body size. This finding is contrary to previous results in smaller animals, where Froude efficiency increased with body size. Although our empirically parameterized estimates for swimming baleen whale drag were higher than those of a simple gliding model, oscillatory locomotion at this scale exhibits generally high Froude efficiency as in other adept swimmers. Our results quantify the fine-scale kinematics and estimate the hydrodynamics of routine and energetically expensive swimming modes at the largest scale.

Measurement of time-varying kinematics of a dolphin in burst accelerating swimming

Dolphins are well known as excellent swimmers for being capable of efficient cruising and sharp acceleration. While studies of the thrust production and power consumption of dolphin swimming have been the main subject for decades, time-varying acceleration process during successive fluke beats still remains poorly understood. In this study, we quantified the time-varying kinematics of a dolphin (Lagenorhynchus obliquidens) by directly recording its burst-accelerating swimming before vertical jump in an aquarium with two synchronized high-speed video cameras. We tracked the three-dimensional trajectories of its beak, body sides, and fluke. We found that dolphin could quickly accelerate from 5.0 m s^-1 to 8.7 m s^-1 merely by 5 strokes (i.e. 2.5 fluke beats) in 0.7 seconds. During the strokes, it was further found that the dolphin demonstrated a great acceleration in downstroke but less acceleration or even a slight deceleration in upstroke. Hydrodynamic forces and thrust power for each stroke were further estimated based on the equation of body motion and a static hydrodynamic model. The drag coefficient of the dolphin was estimated through computational fluid dynamics (CFD) modeling of the steady flows around a realistic geometric model based on 3-D scan data. The thrust and thrust power were then calculated by combining the body kinematics and the drag coefficient, resulting in a maximum stroke-averaged thrust and power-to-mass ratio of 1.3 × 10³ N and 90 W kg^-1 at downstroke, and 3.3 × 10² N and 19 W kg^-1 at upstroke, respectively. Our results point out the importance of asymmetric kinematics in burst acceleration of dolphin, which may be a useful mechanism for biomimetic design of high-performance underwater robots.

Scaling of swimming performance in baleen whales

The scale-dependence of locomotor factors have long been studied in comparative biomechanics, but remain poorly understood for animals at the upper extremes of body size. Rorqual baleen whales include the largest animals, but we lack basic kinematic data about their movements and behavior below the ocean surface. Here we combined morphometrics from aerial drone photogrammetry, whale-borne inertial sensing tag data, and hydrodynamic modeling to study the locomotion of five rorqual species. We quantified changes in tail oscillatory frequency and cruising speed for individual whales spanning a threefold variation in body length, corresponding to an order of magnitude variation in estimated body mass. Our results showed that oscillatory frequency decreases with body length (∝ length−0.53) while cruising speed remains roughly invariant (∝ length0.08) at 2 m s−1. We compared these measured results for oscillatory frequency against simplified models of an oscillating cantilever beam (∝ length−1) and an optimized oscillating Strouhal vortex generator (∝ length−1). The difference between our length-scaling exponent and the simplified models suggests that animals are often swimming non-optimally in order to feed or perform other routine behaviors. Cruising speed aligned more closely with an estimate of the optimal speed required to minimize the energetic cost of swimming (∝ length0.07). Our results are among the first to elucidate the relationships between both oscillatory frequency and cruising speed and body size for free-swimming animals at the largest scale.

Living on the Edge: Settlement Patterns by the Symbiotic Barnacle Xenobalanus globicipitis on Small Cetaceans

The highly specialized coronulid barnacle Xenobalanus globicipitis attaches exclusively on cetaceans worldwide, but little is known about the factors that drive the microhabitat patterns on its hosts. We investigate this issue based on data on occurrence, abundance, distribution, orientation, and size of X. globicipitis collected from 242 striped dolphins (Stenella coeruleoalba) that were stranded along the Mediterranean coast of Spain. Barnacles exclusively infested the fins, particularly along the trailing edge. Occurrence, abundance, and density of X. globicipitis were significantly higher, and barnacles were significantly larger, on the caudal fin than on the flippers and dorsal fin. Barnacles were found more frequently and in greater numbers on the dorsal rather than ventral side of the caudal fin and on the central third of dorsal and ventral fluke surfaces. Nearly all examined individuals attached with their cirral fan oriented opposite to the fluke edge. We suggest that X. globicipitis may chemically recognize dolphins as a substratum, but fins, particularly the flukes, are passively selected because of creation of vortices that increase contact of cyprids with skin and early survival of these larvae at the corresponding sites. Cyprids could actively select the trailing edge and orient with the cirri facing the main direction of flow. Attachment on the dorsal side of the flukes is likely associated with asymmetrical oscillation of the caudal fin, and the main presence on the central segment of the flukes could be related to suitable water flow conditions generated by fluke performance for both settlement and nutrient filtration.

Measurement of hydrodynamic force generation by swimming dolphins using bubble DPIV

Attempts to measure the propulsive forces produced by swimming dolphins have been limited. Previous uses of computational hydrodynamic models and gliding experiments have provided estimates of thrust production by dolphins, but these were indirect tests that relied on various assumptions. The thrust produced by two actively swimming bottlenose dolphins (Tursiops truncatus) was directly measured using digital particle image velocimetry (DPIV). For dolphins swimming in a large outdoor pool, the DPIV method used illuminated microbubbles that were generated in a narrow sheet from a finely porous hose and a compressed air source. The movement of the bubbles was tracked with a high-speed video camera. Dolphins swam at speeds of 0.7 to 3.4 m s−1 within the bubble sheet oriented along the midsagittal plane of the animal. The wake of the dolphin was visualized as the microbubbles were displaced because of the action of the propulsive flukes and jet flow. The oscillations of the dolphin flukes were shown to generate strong vortices in the wake. Thrust production was measured from the vortex strength through the Kutta–Joukowski theorem of aerodynamics. The dolphins generated up to 700 N during small amplitude swimming and up to 1468 N during large amplitude starts. The results of this study demonstrated that bubble DPIV can be used effectively to measure the thrust produced by large-bodied dolphins.

Exploring the mechanics of thunniform propulsion: a model study

Thunniform propulsion is considered a case study in convergent evolution. Independently derived at least four times, it is characterized by uniquely high lift-based thrust and efficient performance. As such, it has been the focus of studies from biologists, engineers, and physicists. Unfortunately, direct physical measurements of this phenomenon are difficult to obtain. Therefore, the majority of research so far has consisted of theoretical modeling or experimental testing with models of low biofidelity. We created a test apparatus that would more accurately mimic thunniform propulsion as seen in the skipjack tuna (Katsuwonus pelamis (L., 1758)). Motion parameters and swimming speeds, as well as caudal fin size, shape, and material properties, were all taken into account and closely matched with in vivo measurements. Instantaneous lateral and in-flow forces were measured in tests over a range of motion regimes. Overall, general motion parameter requirements for thrust generation were determined and quantified. Thrust production, of up to 0.42 N (per whole caudal fin) with a coefficient of thrust of approximately 0.2, were in line with estimates of whole-body drag. Propulsive efficiency estimates were low (≤35%) compared with estimates in the literature of up to 90%. Quasi-static analysis was also conducted and shown to underpredict measured thrust values by up to 50%.

Hydrodynamic flow control in marine mammals

The ability to control the flow of water around the body dictates the performance of marine mammals in the aquatic environment. Morphological specializations of marine mammals afford mechanisms for passive flow control. Aside from the design of the body, which minimizes drag, the morphology of the appendages provides hydrodynamic advantages with respect to drag, lift, thrust, and stall. The flukes of cetaceans and sirenians and flippers of pinnipeds possess geometries with flexibility, which enhance thrust production for high efficiency swimming. The pectoral flippers provide hydrodynamic lift for maneuvering. The design of the flippers is constrained by performance associated with stall. Delay of stall can be accomplished passively by modification of the flipper leading edge. Such a design is exhibited by the leading edge tubercles on the flippers of humpback whales (Megaptera novaeangliae). These novel morphological structures induce a spanwise flow field of separated vortices alternating with regions of accelerated flow. The coupled flow regions maintain areas of attached flow and delay stall to high angles of attack. The delay of stall permits enhanced turning performance with respect to both agility and maneuverability. The morphological features of marine mammals for flow control can be utilized in the biomimetic design of engineered structures for increased power production and increased efficiency.

Passive cambering and flexible propulsors: cetacean flukes

The flukes are the primary locomotor structure in cetaceans, which produce hydrodynamic thrust as the caudal vertebrae are oscillated dorso-ventrally. Effective thrust generation is a function of the kinematics of the flukes, the angle of attack between the flukes and the incident water flow, and the shape of the flukes. We investigated the effect of bending within the caudal region of odontocete cetaceans to determine how changes in angular displacement between caudal vertebrae could effect passive shape change of the flukes. The internal and external changes of bent flukes were examined with computer tomography. Flukes and tailstock were removed from deceased Delphinus delphis, Lagenorhynchus acutus, Peponocephala electra, Phocoena phocoena and Tursiops truncatus, and bent on an adjustable support at 0, 45 and 90 degrees . At 0 degrees , cross-sections of the flukes displayed a symmetrical profile. Cross-sections of bent flukes (45 degrees , 90 degrees ) were asymmetrical and showed a cambered profile. Maximum cambering occurred close to the tailstock and decreased toward the fluke tip. Maximum angular displacement occurred at the 'ball vertebra', which was located posterior of the anterior insertion of the flukes on the tailstock. Bending at the 'ball vertebra' passively cambers the flexible flukes. Cambering could increase hydrodynamic force production during swimming, particularly during direction reversal in the oscillatory cycle.

The axial musculature of Pontoporia blainvillei, with comments on the organization of this system and its effect on fluke-stroke dynamics in the cetacea

The axial muscular system of Pontoporia blainvillei is described and compared with published reports of this system in other cetaceans. A comprehensive system for classification of axial muscles is presented, based on the studies of Slijper. A discrete obliquus capitis inferior is described for the first time in cetacea, and it is suggested that its absence in previous descriptions may have been due partly to dissection error. The major axial muscle-masses are organized in a similar way in most cetaceans, comprising a set of tail elevators and depressors, and a set of tendons with similar actions on the flukes. The anatomy of the axial musculature does not support the idea that the upstroke is the main propulsive stroke in cetaceans, but suggests similar roles of the upstroke and downstroke in propulsion.