Eulerian spatiotemporal correlations in passive scalar turbulence

We study the spatiotemporal two-point correlation function of passively advected scalar fields in the inertial-convective range in three-dimensional homogeneous isotropic turbulence by means of numerical simulations. Our aim is to make a precision test of analytical results recently obtained using functional renormalization group (FRG). We show that at small time delays t, the Eulerian correlations of the scalar decay as a Gaussian in the variable t(p) where p is the wave number, as established by FRG, and which is related to the sweeping effect. At large time delays, a crossover to an exponential decay in t(p)(2) is predicted by the FRG analysis, but not observable in simulations due to numerical noise. We then propose to study this regime for a scalar field advected by a Kraichnan synthetic velocity field, and accurately confirm the FRG result, including the precise form of the prefactor in the exponential. By introducing finite time correlations in the synthetic velocity field, we also uncover the crossover between the two regimes.

Automated summary

We conducted numerical simulations to study the spatiotemporal two-point correlation function of passively advected scalar fields in three-dimensional homogeneous isotropic turbulence. Our aim was to test analytical results obtained using functional renormalization group (FRG). The simulations showed decay of Eulerian correlations of the scalar as a Gaussian at small time delays and a predicted crossover to exponential decay at large time delays, which could not be observed due to numerical noise. We accurately confirmed FRG results by introducing finite time correlations in the synthetic velocity field and studying the crossover between two regimes.