Turbulence is a ubiquitous phenomenon appearing in very different systems over an extremely wide range of scales, from microns to kilometres. In this sense turbulence is not a single problem, but rather a huge field of interdisciplinary research with applications to different disciplines. For example, state of the art simulations of turbulent puffs (see Fig. 1) are applicable to real-life situations and understanding their dynamics is crucial in a variety of situations ranging from industrial processes to pure and applied science.

The FieldTurb initiative is focused on the problem of "Particles and Fields" transported by, and interacting with, complex and turbulent flows. The aim of the project is to gain a better understanding of fundamental questions involving general problems of classical field theories of out-of-equilibrium systems at macro-, micro- and nano-scales, as well as of many applied problems involving, e.g. energy production and transfer, interface functionalization and autonomous navigation. The challenge is to export the knowledge and methodologies developed for the ideal case of Newtonian turbulence to the case of suspensions, foams and emulsions. In general, the objects transported by the flow possess internal degrees of freedom, such as elastic polymers, fibers, or complex particles. One important question is to understand which kind of turbulence emerges from the interactions between the complex constituents of the fluid, and its degree of universality with respect to the detailed microscopic model. The behaviour of particles in complex flows becomes particularly intriguing when particles are active probes, in the sense that they optimise trajectories with respect to some prefixed strategy (see Fig. 2 for an example of active particle trying to catch or stay close to a moving target, like another particle transported by the flow), or simply because they are self-propelled objects (bacteria, biological filaments, artificial swimmers). Both classes of systems pose important challenges from the fundamental point of view of out-of-equilibrium statistical mechanics and open the doors to new generations of devices.

Sometimes, self-prolusion makes the collective dynamics of active particles dramatically different from that of their passive analogues, with new unexpected behaviour such as aggregation in absence of attractive forces, super-fluidic rheological response, spontaneous flow and new motility modes (see Fig. 3). Another line of research, boosted by recent experimental results, is the study of turbulence in quantum fluids. Chaotic/turbulent-like regimes can now be observed in many different superfluid systems, including helium and atomic Bose-Einstein condensates (BECs). Within FieldTurb both theoretical and numerical approaches are used to study 3D and 2D quantum fluids, to assess fundamental universal statistical features of their dynamics.

Also fluid solvers, such as Lattice Boltzmann methods, can be adapted to study relativistic fluids so to offer new insights in apparently distant fields as Plasma Wakefield Acceleration (PWFA). All these problems are tackled by combining traditional tools of theoretical physics with emerging tools at the interface between material science and biology, particularly for active matter applications where new physical concepts arise (e.g. jamming, topological defects). The theoretical approach is complemented by numerical simulations and data analysis, featuring innovative techniques of Machine Learning (ML). In particular, we have been recently using generative methods to fill gapped fluid fields or to generate/expand databases of both Eulerian or Lagrangian data, and used Reinforcement Learning techniques to engineer active particles so to allows them to optimally achieve some tasks.

FieldTurb integrates the expertise of 5 different groups spread on the whole national territory with a long-lasting series of fruitful collaborations, leading to an interwoven network of researchers with many collaborations at the European and international levels.