Stochastic models of Lagrangian acceleration of fluid particle in developed turbulence

TL;DR

This paper reviews simple stochastic models for Lagrangian acceleration in developed turbulence, highlighting their ability to replicate observed non-Gaussian statistics and the dependence on Reynolds number, supported by experimental and numerical data.

Contribution

It introduces and analyzes new Langevin-type stochastic models for Lagrangian acceleration that align with recent experimental and numerical findings.

Findings

Models reproduce non-Gaussian acceleration distributions

Acceleration variance depends on Lagrangian velocity and Reynolds number

Comparison with experimental and numerical data validates the models

Abstract

Modeling statistical properties of motion of a Lagrangian particle advected by a high-Reynolds-number flow is of much practical interest and complement traditional studies of turbulence made in Eulerian framework. The strong and nonlocal character of Lagrangian particle coupling due to pressure effects makes the main obstacle to derive turbulence statistics from the three-dimensional Navier-Stokes equation; motion of a single fluid-particle is strongly correlated to that of the other particles. Recent breakthrough Lagrangian experiments with high resolution of Kolmogorov scale have motivated growing interest to acceleration of a fluid particle. Experimental stationary statistics of Lagrangian acceleration conditioned on Lagrangian velocity reveals essential dependence of the acceleration variance upon the velocity. This is confirmed by direct numerical simulations. Lagrangian intermittency is considerably stronger than the Eulerian one. Statistics of Lagrangian acceleration depends on Reynolds number. In this review we present description of new simple models of Lagrangian acceleration that enable data analysis and some advance in phenomenological study of the Lagrangian single-particle dynamics. Simple Lagrangian stochastic modeling by Langevin-type dynamical equations is one the widely used tools. The models are aimed particularly to describe the observed highly non-Gaussian conditional and unconditional acceleration distributions. Stochastic one-dimensional toy models capture main features of the observed stationary statistics of acceleration. We review various models and focus in a more detail on the model which has some deductive support from the Navier-Stokes equation. Comparative analysis on the basis of the experimental data and direct numerical simulations is made.