Mathematical proof reveals that standard computer simulations of turbulence are fundamentally incorrect and full of 'noise.'
March 31, 2026
Original Paper
Spatial symmetry invariance of solution of Kolmogorov flow
arXiv · 2603.04447
The Takeaway
For decades, scientists have relied on 'Direct Numerical Simulations' to model how air and water flow. This study proves those models lose their physical accuracy almost immediately, meaning much of our existing research into the fine details of turbulence may be based on computer errors rather than reality.
From the abstract
We prove a mathematical theorem that solution for all $t > 0$ of the two-dimensional (2D) Kolmogorov flow governed by Navier-Stokes (NS) equations with periodic boundary condition keeps the same spatial symmetry as its smooth initial condition. The proof of a similar theorem for the three-dimensional NS equations is given in the appendix. These mathematical theorems can be used to check the correctness and reliability of numerical simulations of NS turbulence. For example, they support the corre