Clustering of vector nulls in homogeneous isotropic turbulence

The study of geometrical properties of the velocity, the Lagrangian acceleration, and the vorticity fields in turbulent flows has received considerable attention in the past decades. The geometrical properties of these fields can be useful to model important phenomena in turbulent flows such as superdifusivity, preferential concentration of particles, vortex reconnection, among many others. In this work, we analyze the vector nulls of such vector fields, coming from direct numerical simulations of forced homogeneous isotropic turbulence at $Re_\lambda \in O([40-600])$.  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.