Scaling of conditional Lagrangian time correlation functions of velocity and pressure gradient magnitudes in isotropic turbulence

TL;DR

This study investigates the Lagrangian time correlations of velocity and pressure gradient magnitudes in isotropic turbulence, revealing their dependence on local eddy-turnover time scales and the influence of intermittency corrections.

Contribution

It introduces an analysis of absolute value correlations in turbulence, showing their scaling with eddy-turnover time and the need for intermittency corrections for better data collapse.

Findings

Correlation functions scale with eddy-turnover time, not Kolmogorov time.

Intermittency correction factors improve correlation collapse.

Absolute value correlations are less well collapsed than tensor element correlations.

Abstract

We study Lagrangian statistics of the magnitudes of velocity and pressure gradients in isotropic turbulence by quantifying their correlation functions and their characteristic time scales. It has been found that the Lagrangian time-correlations of the velocity and pressure gradient tensor and vector elements scale with the locally-defined Kolmogorov time scale, defined from the box-averaged dissipation-rate and viscosity. In this work, we study the Lagrangian time-correlations of the absolute values of velocity and pressure gradients. We explore the appropriate temporal scales with the aim to achieve collapse of the correlation functions. The data used in this study are sampled from the web-services accessible public turbulence database(http://turbulence.pha.jhu.edu). The database archives a pseudo-spectral direct numerical simulation of forced isotropic turbulence with Taylor-scale Reynolds number 433, and supports spatial differentiation and spatial/temporal interpolation inside the database. The analysis shows that the temporal evolution of the auto-correlations of the absolute values are determined not by the local Kolmogorov time-scale but by the local eddy-turnover time scale. However, considerable scatter remains and appears to be reduced only after a further (intermittency) correction factor of the form of $(r/L)^\chi$ is introduced where $L$ is the turbulence integral scale. The exponent $\chi$ varies for different variables. The collapse of the correlation functions for absolute values is, however, less satisfactory than the collapse observed for the more rapidly decaying strain-rate tensor element correlation functions.