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 proposed by 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 constant 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.

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• Turbulent mixing