Conditional Lagrangian acceleration statistics in turbulent flows with Gaussian distributed velocities

TL;DR

This paper presents a stochastic model based on a nonlinear Langevin equation to accurately describe Lagrangian acceleration statistics in turbulent flows, aligning well with experimental data and highlighting the effects of velocity-dependent noise intensities.

Contribution

It introduces a novel stochastic framework with velocity-dependent noise terms to model acceleration statistics, supported by exact analytical solutions and extensive data comparison.

Findings

Model accurately reproduces experimental acceleration distributions

Conditional mean acceleration remains small and increases with velocity

Good agreement with high-Reynolds-number Lagrangian data

Abstract

The random intensity of noise approach to one-dimensional Laval-Dubrulle-Nazarenko type model having deductive support from the three-dimensional Navier-Stokes equation is used to describe Lagrangian acceleration statistics of a fluid particle in developed turbulent flows. Intensity of additive noise and cross correlation between multiplicative and additive noises entering a nonlinear Langevin equation are assumed to depend on random velocity fluctuations in an exponential way. We use exact analytic result for the acceleration probability density function obtained as a stationary solution of the associated Fokker-Planck equation. We give a complete quantitative description of the available experimental data on conditional and unconditional acceleration statistics within the framework of a single model with a single set of fit parameters. The acceleration distribution and variance conditioned on Lagrangian velocity fluctuations, and the marginal distribution calculated by using independent Gaussian velocity statistics are found to be in a good agreement with the recent high-Reynolds-number Lagrangian experimental data. The fitted conditional mean acceleration is very small, that is in agreement with DNS, and increases for higher velocities but it departs from the experimental data, which exhibit anisotropy of the studied flow.