Solvable model for space-time correlations of passive scalars advected by turbulent flows with mean velocity
Phys. Rev. Fluids 10, 104607 – Published 24 October, 2025
DOI: https://doi.org/10.1103/x644-pdqq
Abstract
A solvable model for space-time correlations of passive scalars advected by turbulent flows is proposed in the present paper. The model is a combination of Taylor's frozen-flow model and Kraichnan's random-sweeping and white-noise models, namely the Taylor–Kraichnan (TK) model, in which the advection velocity is the sum of a constant mean velocity, a random-sweeping velocity and a white-noise velocity. We find the exact solution of the TK model and consequently obtain analytical expressions for the space-time correlation. These results are used to demonstrate the scale invariance of space-time correlations and the self-similarity of iso-correlation contours in the inertial-convective subrange. In particular, the elliptic approximation to space-time correlations is justified and thus used to rescale spatial and temporal separations, collapsing a family of space-time correlations into a single curve.
