What a single snapshot reveals about the future and the past of turbulent flow

TL;DR

This paper introduces an analytic formalism linking single-time velocity correlations to short-time particle dispersion in turbulence, providing new exact relations and a short-term analog of Richardson's law.

Contribution

It develops a novel formalism that connects Eulerian and Lagrangian turbulence descriptions and derives exact relations for short-time dispersion.

Findings

Derived an exact formula for short-term turbulent dispersion.

Established a conservation law valid even in non-stationary turbulence.

Linked single-time velocity correlations to particle dispersion.

Abstract

We develop an analytic formalism and derive new exact relations that express the short-time dispersion of fluid particles via the single-time velocity correlation functions in homogeneous isotropic and incompressible turbulence. The formalism establishes a bridge between single-time Eulerian and long-time Lagrangian pictures of turbulent flows. In particular, we derive an exact formula for a short-term analog of the long-time Richardson law, and we identify a conservation law of turbulent dispersion which is true even in non-stationary turbulence.