This study investigated factors shaping the thermal sensitivity in antipatharians, a taxon whose members form dense aggregations in all oceans, harbouring a high biodiversity. First, we tested the thermal responses of five sympatric species (Antipathes grandis, Cupressopathes abies, Stichopathes cf. maldivensis, Cirrhipathes anguina and Cirrhipathes cf. spiralis) from the Great Reef of Toliara (Madagascar), using an acute ramping methodology. We then compared the thermal performance curves (TPCs) for oxygen consumption of these five species. Results indicated that phylogeny alone does not explain differences in thermal sensitivity (Antipathidae vs. Myriopathidae). On the contrary, morphology (branched vs. unbranched) appeared as a key factor, with unbranched species (S. cf. maldivensis, C. anguina, C. cf. spiralis) being more tolerant to thermal stress than branched ones (A. grandis and C. abies). Several hypothesis could explain these variations in thermal tolerance across morphology, such as tissue thickness, surface/volume ratio or mass-transfer efficiency. Secondly, we compared the TPC of Stichopathes from Madagascar with those previously obtained in congenerics from the Canary Islands and French Polynesia. This revealed a higher thermal tolerance in the two former than in the latter. It is proposed that it is linked to higher annual temperature variability (but not daily variability) in these two sites compared to French Polynesia. It is concluded that thermal sensitivity in antipatharians is linked to their morphology influencing their physiology and to their thermal history. Phylogeny at the family level plays a less important role in explaining differences in thermal sensitivity in antipatharians.

Line formation of migrating birds is well-accepted to be caused by birds exploiting wake benefits to save energy expenditure. A flying bird generates wingtip trailing vortices that stir the surrounding air upward and downward, and the following bird can get a free supportive lift when positioned at the upward airflow region. However, little to no attention has been paid to clarifying birds’ interests in energy saving, namely, do birds intend to reduce their individual energy consumption or the total energy of the flock? Here, by explicitly considering birds’ interests, we employ a modified fixed-wing wake model that includes the wake dissipation to numerically reexamine the energy saving mechanism in line formation. Surprisingly, our computations show that line formation cannot be explained simply by energy optimization. This remains true whether birds are selfish or cooperative. However, line formations may be explained by strategies optimizing energy cost and either avoiding collision or maintaining vision comfort. We also find that the total wake benefit of the formation attained by selfish birds does not differ much from that got by cooperative birds, the maximum that birds can attain. This implies that selfish birds are still able to fly in formation with very high efficiency of energy saving. In addition, we explore the hypothesis that birds are empathetic and would like to optimize their own energy cost and the neighbors’. Our analysis shows that if birds are more empathetic, the resulting line formation shape deviates more from a straight line, and the flock enjoys higher total wake benefit. Author summary Migratory birds can achieve remarkable performance and efficiency in energy exploitation during annual round-trip migration flight. Theoretical and experimental results have shown that this might be achieved because birds fly together in formation with specific shapes, e.g. the noticeable V formation, to utilize the aerodynamic benefits generated by their flock mates. However, it is still unclear whether energy-guided behavior indeed can lead to these formations. We show that the special formation adopted by migratory birds cannot be explained purely by the energy exploitation mechanism, and that birds’ vision performance and collision avoidance very likely also play important roles in the formation emergence. Our results imply that birds fly together in formation because of energy saving, but the specific shape of the formation depends on non-aerodynamic reasons. The research provides further understandings of the emergence of migratory formation and the energy saving mechanism of animal groups. It may also indicate that wing flapping, currently not considered, has an important effect on the way birds exploit aerodynamic benefits from others during the formation flight.

Extended formation flight is foreseen to be a viable technique for fuel consumption reduction in commercial aviation. It is based on a follower tracking the wake of a leader while maintaining a constant adequate separation. This leads however to different wake dynamics compared to those of the wake of an isolated aircraft. The uncertainty on the relative position between the follower and the wake of the leader further increases the analysis of the underlying vortex dynamics. Using Large Eddy Simulations, this paper presents a methodology to quantify the impact of that uncertainty on the propagation of the formation wake. Midway between a vortex method and grid-based CFD, the Vortex Particle-Mesh method combined the Immersed Lifting Lines is particularly well suited for the simulation of such long-lasting structures. The proposed methodology combines 3D Space Developing and 3D Time Developing simulations to capture the roll-up of the vortex sheets originating from the leader and the follower, their mutual interactions and their long term evolution in a turbulent environment. Simulations are performed for several formation flight configurations around a reference in order to produce a probabilistic representation for the wake propagation. Statistics on the wake vortices characteristics are deduced and are compared to the wake properties of an isolated aircraft.

Formation flight is known for improving the overall aerodynamic efficiency of a pair of aircraft. This work presents a bio-inspired tracking strategy that correctly positions the follower in the wake of the leader in order to optimize the benefits of formation flight, i.e. optimize apparent drag reduction. A simplified aerodynamic model based on Prandtl's lifting line theory enables to compute the 6 degrees-of-freedom dynamics of the follower under the influence of a leader wake. Those dynamics are controlled over time thanks to a speed-control autopilot, while a neural network modifies the speed target according to the follower dynamics. Indeed, the follower dynamic measurements are used to train the neural network through the reinforcement learning framework, drawing inspiration from the trial and error of animal learning. The use of the follower dynamics as unique control measurements ensures a total independence of the tracking method from direct measurements of the leader wake position. Simulations demonstrate the good performances of this new reinforcement learned tracking method when dealing with a simple two-aircraft formation as well as with more challenging configurations involving a larger flock.

In a fuel-efficient extended formation flight of commercial airplanes, the aerodynamic benefits depend on one's ability to surf wake vortices. This paper presents a wake vortex detection scheme based on the exploitation of the aircraft flight dynamics measurements that effectively enables wake surfing. The study focuses on a two-aircraft formation where the follower senses, successfully locates, and tracks the wake produced by the leader over time. The proposed approach relies on an ensemble Kalman filter that propagates a surrogate model of the formation. The model output is here corrected within the estimator through a comparison with measurements of the full six-degree-of-freedom dynamics of the follower, as well as geometric characteristics of the leader. This essentially waives the need for dedicated hardware devices and only requires episodic communication between the leader and the follower. The efficiency of the novel detection strategy is demonstrated using reference data obtained from large-eddy simulations. It is found that the chosen combination of estimator and dynamics measurements is sufficient to detect the position of the impacting wake as long as the dynamics are accurately reproduced by the surrogate model. Additionally, it is shown that a lack of observability hinders the concurrent estimation of the wake position and strength in the presence of uncertainty. Finally, a simulation case evaluates the fuel savings that an active tracking strategy of the optimal relative positioning provides compared with a wake-independent positioning.