A single-time two-point closure based on fluid particle displacements

TL;DR

This paper introduces a novel single-time two-point closure model for turbulence that estimates the Lagrangian timescale using fluid particle displacements, leading to accurate energy spectra and Kolmogorov constant predictions.

Contribution

The paper presents a new closure model based on fluid particle displacements that eliminates ad hoc constants and accurately predicts turbulence energy spectra.

Findings

Energy spectrum aligns with classical scaling

Kolmogorov constant estimated successfully

Model provides a closed set of equations without arbitrary constants

Abstract

A new single-time two-point closure is proposed, in which the equation for the two-point correlation between the displacement of a fluid particle and the velocity allows one to estimate a Lagrangian timescale. This timescale is used to specify the nonlinear damping of triple correlations in the closure. A closed set of equations is obtained without ad hoc constants. Taking advantage of the analogy between particle displacements and scalar fluctuations in isotropic turbulence subjected to a mean scalar gradient, the model is numerically integrated. Results for the energy spectrum are in agreement with classical scaling predictions. An estimate for the Kolmogorov constant is obtained.