Nonlinear hyperbolic balance laws play a central role in the mathematical modelling of fluid-mechanical processes and underpin modern simulation tools for applications ranging from aircraft design to climate research. Despite their importance, fundamental questions remain open, including multi-scale interactions of shocks and shear waves, the influence of randomness, and the well-posedness of multi-dimensional inviscid flow equations in the turbulent, high–Reynolds-number regime. Addressing these challenges requires a close integration of fluid mechanics with analysis, numerics, and stochastics. The Priority Programme 2410 aims to develop new mathematical models and structure-preserving numerical methods to elucidate the dynamic creation of small scales induced by hyperbolic nonlinearity. Its research focuses on novel solution concepts, multi-scale and asymptotic model hierarchies, and probabilistic approaches for hyperbolic systems, laying the foundations for a new numerical paradigm and an improved theoretical understanding of small-scale turbulence.

www.spp2410.uni-stuttgart.de