We consider a uniformly rotating viscous incompressible fluid and estimate particle transport in the vertical direction (parallel to the rotation axis). We prove that for short time and regular initial data, strong rotation suppresses the vertical gradient of flow maps. The proof uses a diffusive Lagrangian formalism, and the suppression of the vertical gradient is a natural and direct byproduct of the formalism.
"Transport in Viscous Rotating Fluids." Commun. Math. Sci. 2 (4) 673 - 684, December 2004.