Non-Equilibrium Turbulence in the Post-Kolmogorovean era – A Combined Empirical-Theoretical Approach

Clara Velte, Associate Professor, Fluid Mechanics, Coastal and Maritime Engineering, Technical University of Denmark (DTU), Denmark

Turbulence remains one of the most important unsolved problems in classical physics. As in many other branches of physics, equilibrium descriptions are prevalent, yet it is the non-equilibrium states that dominate nature and engineering and often govern the most critical dynamics. The classical framework – shaped by Richardson, Kolmogorov, and Batchelor and commonly referred to as K41 – rests on assumptions of local equilibrium. While this produces reliable predictions under near-equilibrium conditions, it fails to capture flows that evolve strongly in space and time, where memory effects, inhomogeneities, and non-local interactions dominate.

In this talk, I will present recent progress towards a post-Kolmogorov understanding of turbulence, based on a combined empirical–theoretical program. Building on Galilei symmetries in the spirit of Emmy Noether, we are formulating a first-principles theory of non-equilibrium turbulence, designed to capture the dynamics beyond K41. This theoretical framework is being directly validated through extensive state-of-the-art experiments, enabling us to uncover the mechanisms that govern energy and momentum transfer in evolving flows. I will conclude by outlining how this approach paves the way for improved models of turbulence and opens new perspectives for tackling one of physics’ enduring frontiers.