On the small-scale structure of turbulence and its impact on the pressure field

TL;DR

This paper investigates the small-scale structures in turbulence and their influence on the pressure field, revealing how intense regions affect pressure non-locally across different scales and Reynolds numbers.

Contribution

It provides a quantitative analysis of the spatial distribution of velocity gradient structures and their impact on the pressure field in turbulent flows.

Findings

Correlation length proportional to Kolmogorov scale

Intense rotation regions influenced by dissipation-scale neighborhoods

Strain-dominated regions affected by inertial-scale neighborhoods

Abstract

Understanding the small-scale structure of incompressible turbulence and its implications for the non-local pressure field is one of the fundamental challenges in fluid mechanics. Intense velocity gradient structures tend to cluster on a range of scales which affects the pressure through a Poisson equation. Here we present a quantitative investigation of the spatial distribution of these structures conditional on their intensity for Taylor-based Reynolds numbers in the range [160, 380]. We find that the correlation length, the second invariant of the velocity gradient, is proportional to the Kolmogorov scale. It also is a good indicator for the spatial localization of intense enstrophy and strain-dominated regions, as well as the separation between them. We describe and quantify the differences in the two-point statistics of these regions and the impact they have on the non-locality of the pressure field as a function of the intensity of the regions. Specifically, across the examined range of Reynolds numbers, the pressure in strong rotation-dominated regions is governed by a dissipation-scale neighbourhood. In strong strain-dominated regions, on the other hand, it is determined primarily by a larger neighbourhood reaching inertial scales.