Solvable model for space-time correlations of passive scalars advected by turbulent flows with mean velocity

The space-time decorrelation of a passive scalar advected by turbulent flows is dominated by three physical processes: mean-flow carrying downstream, large-eddy random sweeping, and small-eddy distortion. Each process has been investigated through Taylor's frozen-flow hypothesis and Kraichnan's random-sweeping and white-noise models. However, their coupling effects remain unexplored. The present paper proposes the Taylor--Kraichnan model to represent the coupled effects of the three processes and leads to the exact solution of space--time correlation. The scale invariance of the space--time correlation is found and consistent with the elliptical approximation model.