Clustering of vector nulls in homogeneous isotropic turbulence

TL;DR

This study investigates the spatial clustering of vector nulls in turbulent flows, revealing differences among velocity, acceleration, and vorticity nulls, and explores their behavior across different Reynolds numbers and inertial particle concentrations.

Contribution

It provides a detailed analysis of null point clustering in turbulence and links inertial particle clustering to acceleration nulls, advancing understanding of turbulence structures.

Findings

Velocity nulls cluster more strongly than acceleration and vorticity nulls.

Acceleration and vorticity nulls are denser than velocity nulls.

Inertial particles show clustering patterns similar to acceleration nulls.

Abstract

We analyze the vector nulls of velocity, Lagrangian acceleration, and vorticity, coming from direct numerical simulations of forced homogeneous isotropic turbulence at $Re_\lambda \in [40-610]$. We show that the clustering of velocity nulls is much stronger than those of acceleration and vorticity nulls. These acceleration and vorticity nulls, however, are denser than the velocity nulls. We study the scaling of clusters of these null points with $Re_\lambda$ and with characteristic turbulence lengthscales. We also analyze datasets of point inertial particles with Stokes numbers $St = 0.5$, 3, and 6, at $Re_\lambda = 240$. Inertial particles display preferential concentration with a degree of clustering that resembles some properties of the clustering of the Lagrangian acceleration nulls, in agreement with the proposed sweep-stick mechanism of clustering formation.