PID2025.Fanelli

Objective:

The GHOST project centers on the mathematical study of systems of fluids in presence of large heterogeneities. The main focus is on models arising from two different, but at the same time interrelated, domains: geophysical fluid dynamics and turbulence theory. This project is anchored in the observation that geophysical and turbulent flows share many heterogeneity features: presence of multiple scales and boundary effects, appearance of low regularity structures, variations of inner properties of the fluid. The leitmotif underlying GHOST is the idea that non-homogeneities are the main factor determining non-trivial effects in the dynamics. However, going beyond the usual approximation of small variations from the homogeneous situation represents a challenge at the theoretical level: GHOST addresses this by proposing a novel approach. The core of the GHOST strategy lies in the idea that large heterogeneities are tied to some sort of geometric information: GHOST's ultimate aim is to understand this information and the interplay between the geometry of the problem and the mean flow, in order to give an accurate description of the resulting dynamics. This will be achieved by the development of advanced analytical techniques and the identification of relevant models capable of describing geophysical and turbulent flows in different regimes. To reach this ambitious objective, GHOST identifies three specific goals: (1) description of geometric constraints on the dynamics in presence of large heterogeneities; (2) derivation of reduced models in presence of multiple scales, and description of the interaction of those scales; (3) study of boundary effects: non-homogeneous boundary conditions for open systems, and also propagation of sharp fronts; (4) study of systems in presence of degeneracies (vacuum, transition parabolic-hyperbolic). Owing to the intrinsic applied nature of the questions standing at the basis of the project, the realisation of the GHOST scientific programme will have a broad and deep resonance on both the mathematical and physical communities. While advancing the theoretical understanding of non-homogeneous fluid dynamics, GHOST will also impact neighbouring fields, such as geophysics, meteorology and astrophysics, paving the way for more accurate predictions and new investigations in those directions.