# Direct assessment of Kolmogorov's first refined similarity hypothesis

## TL;DR

This study provides the first conclusive experimental and numerical evidence supporting Kolmogorov's first refined similarity hypothesis, demonstrating the universality of local velocity increment distributions across scales in turbulent flows.

## Contribution

It offers the first direct experimental and numerical validation of Kolmogorov's first refined similarity hypothesis using three-dimensional velocity measurements.

## Key findings

- Distributions of velocity increments collapse when scaled by local Reynolds number.
- Supports universality of the refined similarity hypothesis.
- Provides conclusive experimental evidence for the hypothesis.

## Abstract

Using volumetric velocity data from a turbulent laboratory water flow and numerical simulations of homogeneous, isotropic turbulence, we present a direct experimental and numerical assessment of Kolmogorov's first refined similarity hypothesis based on three-dimensional measurements of the local energy dissipation rate $\epsilon_r$ measured at dissipative scales $r$. We focus on the properties of the stochastic variables $V_L = \Delta u(r)/(r \epsilon_r)^{1/3}$ and $V_T = \Delta v(r)/(r\epsilon_r)^{1/3}$, where $\Delta u(r)$ and $\Delta v(r)$ are longitudinal and transverse velocity increments. Over one order of magnitude of scales $r$ within the dissipative range, the distributions of $V_L$ and $V_T$ from both experiment and simulation collapse when parameterised by a suitably defined local Reynolds number, providing the first conclusive experimental evidence in support of the first refined similarity hypothesis and its universality.