Velocity gradients statistics along particle trajectories in turbulent flows: the refined similarity hypothesis in the Lagrangian frame

TL;DR

This study tests the refined similarity hypothesis in turbulent flows by analyzing velocity gradient statistics along particle trajectories, revealing different behaviors for particles with small versus large inertia.

Contribution

The paper rephrases and tests the refined similarity hypothesis in the Lagrangian frame using high-resolution numerical simulations, providing new insights into particle inertia effects.

Findings

Lagrangian RSH verified for small inertia particles at large time lags.

Eulerian RSH holds for large inertia particles approaching ballistic behavior.

Numerical simulations reach Reynolds number up to 400 with 2048^3 grid points.

Abstract

We present an investigation of the statistics of velocity gradient related quantities, in particluar energy dissipation rate and enstrophy, along the trajectories of fluid tracers and of heavy/light particles advected by a homogeneous and isotropic turbulent flow. The Refined Similarity Hypothesis (RSH) proposed by Kolmogorov and Oboukhov in 1962 is rephrased in the Lagrangian context and then tested along the particle trajectories. The study is performed on state-of-the-art numerical data resulting from numerical simulations up to Re~400 with 2048^3 collocation points. When particles have small inertia, we show that the Lagrangian formulation of the RSH is well verified for time lags larger than the typical response time of the particle. In contrast, in the large inertia limit when the particle response time approaches the integral-time-scale of the flow, particles behave nearly ballistic, and the Eulerian formulation of RSH holds in the inertial-range.