Space-time correlations of passive scalars in colored-noise flows

TL;DR

This paper derives an analytical solution for the space-time correlation of passive scalars in colored-noise flows, validating the elliptic approximation and clarifying decorrelation mechanisms.

Contribution

It provides a new analytical solution that extends the elliptic approximation to colored-noise flows, capturing both spatial and temporal scalar correlations.

Findings

Validates the elliptic approximation model for colored-noise flows.

Recovers Obukhov--Corrsin scaling under Kolmogorov velocity spectra.

Shows Gaussian temporal decorrelation due to large-scale sweeping.

Abstract

The space-time correlation of a passive scalar advected by a Gaussian colored-noise velocity with wavenumber-dependent correlation times and power-law spatial spectra is investigated in the present paper. Within the inertial-convective subrange, we derive an analytical solution for the space-time correlation. This solution validates the elliptic approximation (EA) model [He and Zhang, Phys. Rev. E 73, 055303(R) (2006)], demonstrating that the iso-correlation contours are self-similar in the co-moving space-time frame $(r-U\tau, V\tau)$, with a universal spatial-to-temporal intercept ratio of 1.55. Unlike the classic Kraichnan white-noise model, our formulation simultaneously recovers the Obukhov--Corrsin scaling for spatial correlations (when the velocity obeys Kolmogorov scaling) and reproduces the random-sweeping mechanism, yielding Gaussian (rather than exponential) temporal decorrelation of scalar Fourier modes. Our results clarify the underlying decorrelation mechanism of passive scalars: mean-flow advection and large-scale sweeping dominate temporal decorrelation, and small-scale distortion dominates spatial decorrelation.