Eulerian spatio-temporal correlations in passive scalar turbulence

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 $t{p}^2$ 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.

10 pages, 10 figures

References in corpus (5)

• The nonperturbative functional renormalization group and its applications
• Spatiotemporal velocity-velocity correlation function in fully developed turbulence
• Scaling, renormalization and statistical conservation laws in the Kraichnan model of turbulent advection
• Spatio-temporal correlations in 3D homogeneous isotropic turbulence
• Spatio-temporal correlation functions in scalar turbulence from functional renormalization group

Cited by in corpus (6)

• Functional renormalisation group for turbulence
• The unpredicted scaling of the one-dimensional Kardar-Parisi-Zhang equation
• Spatio-temporal correlation functions in scalar turbulence from functional renormalization group
• The inviscid fixed point of the multi-dimensional Burgers-KPZ equation
• Functional renormalisation group approach to shell models of turbulence
• The non-perturbative sides of the Kardar-Parisi-Zhang equation