Transport in finite size systems: An exit time approach

Connectivity Analysis Applied to Mesoscale Eddies in the Western Mediterranean Basin

The Western Mediterranean basin (WMED) is characterized by the presence of energetic and dynamic mesoscale cyclonic and anticyclonic eddies. They mainly originate along the Algerian and the Northern currents and have a large influence on the basin circulation. Eddies can last for months, with longer lifetimes associated with the anticyclones, which can move far from their areas of origin. As they partially isolate and transfer water masses, they also have an impact on water properties (physical, chemical and biological), pollutant’s dispersion and transport of eggs, larvae and planktonic organisms. In this study, a connectivity analysis method is applied to the anticyclonic eddies (AEs) identified by an automated hybrid detection and tracking algorithm south of 42°N in the WMED. The same methodology is also applied to the trajectories of Lagrangian surface drifters available in the study area. The purpose is to highlight the connections between different areas of the basin linked to eddy activities in addition to the connectivity due to the mean surface circulation. Drifter data analysis showed that all the WMED sub-basins are strongly interconnected, with the mean surface circulation allowing a shortcut connection among many areas of the basin. The connectivity analysis of the AEs tracks shows that although AEs are ubiquitous in the WMED, their connectivity is limited to well-defined regions, depending on their origin location. Three main regions: the south-western, the south-eastern and the northern parts of the basin are characterized by AEs recirculation, with sporadic export of eddies to the other WMED zones.

Zermelo's problem: Optimal point-to-point navigation in 2D turbulent flows using reinforcement learning

To find the path that minimizes the time to navigate between two given points in a fluid flow is known as Zermelo's problem. Here, we investigate it by using a Reinforcement Learning (RL) approach for the case of a vessel that has a slip velocity with fixed intensity, V_s, but variable direction and navigating in a 2D turbulent sea. We show that an Actor-Critic RL algorithm is able to find quasioptimal solutions for both time-independent and chaotically evolving flow configurations. For the frozen case, we also compared the results with strategies obtained analytically from continuous Optimal Navigation (ON) protocols. We show that for our application, ON solutions are unstable for the typical duration of the navigation process and are, therefore, not useful in practice. On the other hand, RL solutions are much more robust with respect to small changes in the initial conditions and to external noise, even when V_s is much smaller than the maximum flow velocity. Furthermore, we show how the RL approach is able to take advantage of the flow properties in order to reach the target, especially when the steering speed is small.

On the relationship between fractal dimension and encounters in three-dimensional trajectories

The encounter of individuals-prey, predators and mates-living in the surrounding environment is a fundamental process in the life of an organism. Along with the sensory abilities, this process will be regulated by the movement rules adopted by the individual. In this work we discuss the encounter-enhancement effect due to different natatorial modes by calculating the number of encounters realised by differently convoluted trajectories in two homogeneous distributions of particles. Using numerically generated trajectories representative of specific swimming behaviour, we demonstrate that high values of three-dimensional fractal dimension D(3D)(>1.9) are beneficial only at high concentration, whereas at low concentration less tortuous tracks (D(3D) approximately 1.5) are almost equally efficient. In the light of our results it is possible to better understand the behavioural adaptations evolved by individuals to thrive in their environment.