Empirical large-scale extension of Yakhot's model of strong turbulence

TL;DR

This paper extends Yakhot's turbulence model empirically to accurately describe velocity increment statistics across all scales up to the system size, incorporating new parameters fixed by boundary conditions, and aligns well with experimental data.

Contribution

It introduces an empirical extension of Yakhot's model with additional parameters to capture large-scale turbulence statistics, ensuring correct boundary behavior.

Findings

Model accurately describes velocity statistics up to system size

Parameters are physically motivated and boundary-fixed

Good agreement with experimental turbulence data

Abstract

We propose an empirical extension of Yakhot's model of strong turbulence [V. Yakhot, Phys. Rev. E 57(2) (1998)] that correctly describes the statistics of longitudinal velocity increments not only in the inertial range but also for larger scales up to the system length scale L. Two additional parameters are introduced to the original equation for the probability density function of velocity increments. These parameters can be motivated by physical arguments and their values are fixed by large scale boundary conditions. The resultant model ensures correct convergence of structure functions at the system length scale, including vanishing slopes at L, and shows good agreement with experimental data.