smasH

The main purpose of smasH is to understand the emergence of small-scale structures (like the celebrated -5/3 law for isotropic homogenous turbulence) in hydrodynamics and their generic persistence. Such a behavior will be fully tested on local and non-local PDE toy models. The insight gained on those models will be challenged through numerical experiments on more physically realistic models to identify the ideas and technical aspects that can be generalized. In particular, our aim is to test the hypothesis that scaling laws emerge as a scale-by-scale average of finer microlocal dynamics and small-scale features. We will clarify the respective roles of strong local non-linear interactions and mild global couplings The novelty of smasH lies in a collaborative paradigm involving mathematical models and a precise understanding of their qualitative behaviors. The whole process will be guided and backed both by new numerical experiments and by the expertise acquired on physically realistic models by some members of the consortium. The unique synergy of the team, both at the scientific and personal level, provides a strong backbone to the project smasH The project needs to gather expertise in mathematical physics, microlocal analysis and numerical simulations. The consortium is composed of 17 distinguished scientists who bring to the project specific and complementarity skills well adapted to the different work packages. They have already demonstrated their ability to work together as attested by the many ongoing collaborations within the consortium, and their willingness to share their expertise with younger scientists. The consortium will be organized into three geographic teams (Reims, Lyon, Paris) and is composed of 2 members at the doctoral level, 9 young experts (2 of them currently preparing their habilitation theses) and 6 senior researchers. The completion of the project will contribute to the training of 1 new PhD students, 2 post-docs and 4 master students