Lagrangian and Eulerian velocity structure functions in hydrodynamic turbulence

TL;DR

This paper derives analytical scaling relations for Lagrangian and Eulerian velocity structure functions in turbulence, matching recent experimental and numerical data without relying on dimensional analysis.

Contribution

It provides the first analytical calculation of scaling exponents for these structure functions directly from the Navier-Stokes equations.

Findings

Scaling relations hold within the inertial range.

Analytical exponents agree with experimental data.

No dimensional assumptions used in derivation.

Abstract

The Lagrangian and Eulerian transversal velocity structure functions of fully developed fluid turbulence are found basing on the Navier-Stokes equation. The structure functions are shown to obey the scaling relations inside the inertial range. The scaling exponents are calculated analytically without using dimensional considerations. The obtained values are in a very good agreement with recent numerical and experimental data.