Week 20.01.2025 – 26.01.2025

Decaying turbulence, characterized by energy dissipation from an initial high-energy state, remains a fundamental challenge in classical physics. This work presents an exact analytical solution to the Navier-Stokes (NS) equations for incompressible fluid flow in the context of decaying turbulence, introducing the novel framework of the \textit{Euler ensemble}. This framework maps turbulent dynamics onto discrete states represented by regular star polygons with rational vertex angles in units of 2π. A key feature of the Euler ensemble is a duality between classical turbulence and a hidden one-dimensional quantum system, analogous to the AdS/CFT correspondence in quantum field theory. This duality enables the derivation of exact turbulence statistics, replacing traditional heuristic scaling laws with universal results derived directly from the NS equations. For example, the decay law for turbulent kinetic energy is predicted as $ E(t)∼t^{−5/4}$, with quantitative agreement to within 1% standard deviation in experimental and numerical data. The framework is validated using Direct Numerical Simulations (DNS) and experimental results, including grid turbulence and large-tank experiments. Additionally, the Euler ensemble predicts novel macroscopic quantum-like effects, such as oscillations in the decay index as a function of the scaling variable $r/\sqrt t$. These predictions highlight new avenues for experimental and numerical exploration of turbulence. This work addresses long-standing challenges in turbulence theory, providing a rigorous, universal description of decaying turbulence with applications across fluid dynamics, geophysics, and engineering.