Stochastic modeling of Fourier modes in two-dimensional turbulence via filtered white noise

TL;DR

This paper investigates the statistical structure of Fourier modes in 2D turbulence, proposing a stochastic model based on filtered white noise and validating it through numerical simulations of passive tracer transport.

Contribution

It introduces a novel stochastic model for Fourier components in 2D turbulence, capturing key statistical features and improving understanding of turbulent transport.

Findings

Identification of a typical time correlation length in Fourier modes

Development of a stochastic model that replicates turbulence statistics

Validation of the model through comparison with direct numerical simulations

Abstract

Modeling turbulent flows by a random Fourier decomposition is a classical procedure in order to use simplified models of turbulence in heat transport and other applications. We carefully investigate the Fourier time series of two-dimensional turbulent flows forced at intermediate scales and identify significant statistical structures. In particular, we find the existence of a typical time correlation length, and propose a stochastic model for the Fourier components. Finally, we compute the transport of a passive tracer under purely convective dynamics by means of direct numerical simulation of the turbulent flow and compare it with the effective diffusion produced by the stochastic model.