Eulerian spatio-temporal correlations in passive scalar turbulence

TL;DR

This paper investigates the spatio-temporal correlations of passive scalar fields in turbulence, confirming theoretical predictions through numerical simulations and exploring the crossover between Gaussian and exponential decay regimes.

Contribution

It provides numerical validation of the FRG analysis for scalar correlations and examines the effects of finite velocity correlation times.

Findings

Gaussian decay at small times in tp

Exponential decay at large times in tp^2

Crossover behavior with finite velocity correlations

Abstract

We study the spatio-temporal two-point correlation function of passively advected scalar fields in the inertial-convective range in three dimensions by means of numerical simulations. We show that at small time delays $t$ the correlations decay as a Gaussian in the variable $tp$ where $p$ is the wavenumber. At large time delays, a crossover to an exponential decay in $tp^2$ is expected from a recent functional renormalization group (FRG) analysis. We study this regime for a scalar field advected by a Kraichnan's ``synthetic'' velocity field, and accurately confirm the FRG result, including the form of the prefactor in the exponential. By introducing finite time correlations in the synthetic velocity field, we uncover the crossover between the two regimes.