# Kolmogorov's Lagrangian similarity law newly assessed

## TL;DR

This paper uses advanced DNS to validate Kolmogorov's Lagrangian turbulence theory, confirming the universal constant of the second order Lagrangian velocity structure function with high confidence.

## Contribution

It introduces hyperviscous DNS at higher Reynolds numbers to accurately assess Kolmogorov's Lagrangian similarity law and determine the universal constant C_0.

## Key findings

- Hyperviscous simulations accurately predict LVSF-2 in inertial range.
- Strong support for Kolmogorov's Lagrangian similarity assumption.
- Universal constant C_0 estimated as 7.5 ± 0.2.

## Abstract

Kolmogorov's similarity turbulence theory in a Lagrangian frame is assessed with new direct numerical simulations (DNS) of isotropic turbulence with and without hyperviscosity, which attain higher Reynolds numbers than previously available. It is demonstrated that hyperviscous simulations can be used to accurately predict second order Lagrangian velocity structure function (LVSF-2) in the inertial range. The results give strong support for Kolmogorov's Lagrangian similarity assumption and allow to compute the universal constant of the LVSF-2, which gives $C_0=7.5 \pm 0.2$, with a new level of confidence.