The Euler ensemble represents turbulence as a random walk on a discrete star polygon, forming a solvable string theory. This structure predicts a universal turbulent decay law \(E(t) \sim t^{-5/4}\), replacing heuristic scaling laws with a mathematically exact result.

The Euler ensemble replaces the heuristic Kolmogorov K41 scaling with an exact momentum loop equation (MLE) solution, predicting a new universal velocity scaling law. Direct Numerical Simulations (DNS) confirm deviations from K41 and show excellent agreement with the predicted fractal structure of turbulence.