Eulerian spatio-temporal correlations in passive scalar turbulence

• DOI: 10.48550/arxiv.2104.12453
• Publication Date: 2021-12-22
• Authors: Anastasiia Gorbunova; Carlo Pagani; Guillaume Balarac; Léonie Canet; Vincent Rossetto
• Keywords: Statistical Mechanics (cond-mat.stat-mech); 0103 physical sciences; Fluid Dynamics (physics.flu-dyn); 500; FOS: Physical sciences; Physics - Fluid Dynamics; 01 natural sciences; [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph]; Condensed Matter - Statistical Mechanics

10 pages, 10 figures<br/>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.<br/>