Spontaneous stochasticity in the fluctuating Navier-Stokes equations on a logarithmic lattice.

Authors

Erika Paola Ortiz Bernal, Ciro S Campolina, Alexei A Mailybaev

Published in

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences. Volume 384. Issue 2325. Jul 30, 2026.

Abstract

The predictability of turbulent flows remains a challenging problem for mathematicians, physicists and meteorologists. In this context, we consider the three-dimensional incompressible Navier-Stokes equations with small-scale random forcing on logarithmic lattices in Fourier space. Our goal is to probe the phenomenon of spontaneous stochasticity in this system, which means that its solutions remain stochastic in the limit of vanishing viscosity and noise. For this, we consider numerical simulations with increasing Reynolds numbers and vanishing noise amplitudes. Through measurements of statistics of individual large-scale Fourier modes, we verify the spontaneous stochasticity in two different setups: from rough initial data, and after a finite-time blowup of a strong solution. The convergence of probability density functions for distinct parameters suggests that the limiting solution is a universal stochastic process. This article is part of the theme issue 'Frontiers of turbulence and statistical physics'.

PMID:
42531309
Bibliographic data and abstract were imported from PubMed on 31 Jul 2026.

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