SCIENCE NON LINÉAIRE

023 will be the bicentenary of Navier’s work that led to the establishment of the master equations of fluid mechanics, known as the Navier-Stokes equations, which are intrinsically linked to Turbulence, certainly one of the most common phenomena around us but also one of the most complex fields in physics. Far from being purely symbolic, this anniversary is an important event and the opportunity to take stock of the evolution of Navier-Stokes Turbulence research over 200 years and of its future prospects. Because of their age, the Navier-Stokes equations are often ambiguously qualified as "classic", thus risking the suggestion that nothing important remains to be discovered in fluid mechanics, whereas paradoxically, despite 200 years of active research, the discipline retains an unwavering youth. On the one hand, because the complexity of the Navier-Stokes equations means that study remains of central and broad relevance, their mathematical properties and physical implications remaining far from having been fully disclosed, in particular when it comes to the understanding of turbulent flows. On the other hand, because the major contemporary challenges that humankind must urgently face, such as climate, the environment, ecological transition and public health are inseparable from the need for major scientific advances in the understanding and modelling of Navier-Stokes Turbulence. Indeed, the bicentenary of the Navier-Stokes equations reminds us that their very birth carries the trace of an intrinsic interconnectedness as Navier was both a mathematician and a bridge engineer, anticipating a long inter-and-multi-disciplinary tradition. Ranked among the 7 mathematical problems of the millennium by the Clay society, the Navier-Stokes equations is also often cited as one of the most important equations in physics and remains at the heart of many natural sciences and industrial applications. The bicentennial of the Navier-Stokes equations also comes at a time when Turbulence research appears to have reached a certain degree of maturity, manifested in particular by the increasing number if bridges the discipline has built with other fields of science. Concepts intimately associated to the physics of Navier-Stokes Turbulence are now commonly linked to other disciplines as varied as quantum mechanics, wave physics, optics, active matter, granular media, etc. well beyond the physics of flows. It is to be hoped that these transdisciplinary bridges will also, in turn, contribute to fostering fundamental advances in unravelling the mysteries of the Navier-Stokes equations. The aim of this school is to provide to Phd students, post-docs and young scientists lectures given by world experts on fundamentals aspects Navier-Stokes turbulence, reviewing both the accumulated knowledge over the past 200 years and the remaining challenges, open questions and new fields to be explored by next generations of scientists.