From additive to transport noise in 2D fluid dynamics

TL;DR

This paper demonstrates how multiscale analysis can rigorously derive transport noise from additive noise in 2D fluid dynamics models, linking small-scale stochastic perturbations to large-scale transport phenomena.

Contribution

It introduces a rigorous multiscale framework connecting additive noise in fluid equations to transport noise, applicable to both passive scalars and the fluid itself.

Findings

Convergence of stochastic characteristics in the infinite scale separation limit.

Derivation of transport noise from additive noise through multiscale arguments.

Application to stochastic 2D Euler equations with additive noise.

Abstract

Additive noise in Partial Differential equations, in particular those of fluid mechanics, has relatively natural motivations. The aim of this work is showing that suitable multiscale arguments lead rigorously, from a model of fluid with additive noise, to transport type noise. The arguments apply both to small-scale random perturbations of the fluid acting on a large-scale passive scalar and to the action of the former on the large scales of the fluid itself. Our approach consists in studying the (stochastic) characteristics associated to small-scale random perturbations of the fluid, here modelled by stochastic 2D Euler equations with additive noise, and their convergence in the infinite scale separation limit.