Turbulence and Mixing in Fluid Dynamics

The goal of this workshop is to bring together junior and senior researchers at the forefront of mathematical investigations into the dynamical behavior of fluid flow. Recent years have seen rapid progress on fundamental issues connecting to the theory of turbulence and mixing dynamics. For the classical fluid equations of Euler and Navier-Stokes, key advances range from foundational questions related to well-posedness – such as the constructions of irregular and nonunique solutions, or finite time singularity formation – to a precise analysis of (meta) stable as well as unstable dynamics and the behavior of special solutions. Hereby, a quantitative understanding of mixing or shearing mechanisms has been a crucial ingredient which plays an important role in passive and active advection (e.g. for exponential mixing or dissipation enhancement), shedding some light on anomalous dissipation as it is relevant in connection to Kolmogorov’s theory of turbulence, as well as clarifying certain stabilizing effects.
These recent developments have brought within reach an analysis of previously elusive topics concerning the longtime dynamics (such as scaling laws of turbulence, dissipation anomalies or metastable behaviors). This workshop will pave the way for new progress in these directions by enabling an exchange on the central ideas and techniques underlying the various advances on different aspects.