Fluids, in complex regimes, show random features. The aim of this project is approaching several questions around the randomness of fluids by means of a theory that could be called “Stochastic Fluid Mechanics”. The distinctive feature of this theory, opposite to others that investigated the stochastic features of fluids, is that it is based on the usual continuum mechanics equations, in particular the Navier-Stokes and Euler equations, but suitably modified by the presence of random elements, like an additive or a transport type noise. Stochastic equations of fluid dynamics have been studied already for three decades and the number of foundational results is very large. However, two basic directions have been explored only partially: a) the origin and the form of noise in fluids b) the consequences of the presence of noise. This project will make progresses in these two directions, describing the noise near boundary due to vortex productions, including the question of intrinsic stochasticity at the boundary, the propagation of additive noise at small scales to a transport-stretching noise at large scales, the consequences of transport noise on eddy viscosity, enhanced dissipation, enhanced coalescence, and other applications in turbulence and Geophysics. The most ambitious core of the project is putting together these pieces in a picture that explains the mechanism of regularization by noise for the 3D Navier-Stokes equations. The additive noise at small scales is responsible for a transport-stretching noise at larger scales which could prevent blow-up of high intensity vortex structures. We have already proved recently that a noise, of transport type only, has this regularization effect, but stretching amplifies vorticity and new progresses are needed to cope with both processes. We aim to use the experimentally observed fact that small scale velocity should be approximately orthogonal to vorticity in high intensity regions.

When and how did the first galaxies form across cosmic history? Were they different from present-day ones? This is only a small subset of key cosmological questions that the combination of deep galaxy observations, theoretical modeling, and powerful simulations envisaged here will allow us to answer for the first time. Deep galaxy surveys have provided a first valuable characterization of early galaxies in the Epoch of Reionization (redshift z > 6), mostly in terms of their stellar content. However, almost nothing is known about their internal structure and Interstellar Medium (ISM). This is in striking contrast with galaxies at z < 2, for which ISM observations have enabled a much more complete physical description. Hence, a substantial progress in the study of early galaxies must be based on techniques able to probe their ISM. Conversely, ISM studies will help completing the “stellar” picture. Interstellar will bridge this gap. Its main aim is to understand the internal structure and interstellar medium of galaxies in the Epoch of Reionization by performing theoretical modeling and high fidelity simulations. By post-processing the simulations and calibrating them with local analogs, we will produce mock images/spectra used to (i) interpret available high-redshift observations, and (ii) plan breakthrough experiments with ALMA, JWST and E-ELT. The advent of ALMA, JWST, E-ELT and advances in computational cosmology make the study of high-z ISM one of the most promising areas of development in cosmology. The aim will be achieved through 5 objectives distributed among 3 Work Packages (WPs). WP1 is concerned with theoretical work, a preparatory phase for the cosmological simulations performed in WP2. WP2 represents the production phase of the project and will deliver cutting-edge zoom simulations of a sample of high-z galaxies and their ISM. Finally, WP3 is concerned with the exploitation of the numerical results and their integration with observations.