Clustering of vector nulls in homogeneous isotropic turbulence

Abstract

We analyze the vector nulls of velocity, Lagrangian acceleration, and vorticity, coming from direct numerical simulations of forced homogeneous isotropic turbulence at Re λ ∈ 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 λ and with characteristic turbulence lengthscales.We also analyze datasets of point inertial particles with Stokes numbers St = 0.5, 3, and 6, at Re λ = 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.

Phase ordering, topological defects, and turbulence in the 3D incompressible Toner-Tu equation

“…2(b)]. Furthermore, the visible clustering of defects at high-Re is consistent with the observed clustering of vector nulls in fluid turbulence [26].…”

“…We locate defects using the algorithm prescribed by Berg and Lüscher [24] that has been successfully used to study: (a) the role of defects in the 3D Heisenberg transition [13], and (b) coarsening dynamics in the 3D Ginzburg-Landau equations [12]. Similar algorithms have also been used to identify vector nulls in magnetohydrodynamics [25], and fluid turbulence [26]. In Fig.…”

Scale-dependent particle clustering in transitional wake flow

“…An extensive 'sweep-stick' mechanism for 3-D HIT at high Re was subsequently proposed (Coleman & Vassilicos 2009), in which a particle cluster mimics the sticking zero-acceleration points in the flow field causing two particles to converge to each other regardless of Sk. A recent study by Mora et al (2021) compares the clustering of three vector nulls, i.e. stagnation points of velocity, Lagrangian acceleration and vorticity, in terms of the scaling properties and Re dependence.…”

“…They questioned the validity of the sweep-stick mechanism by the observation of evident non-zero accelerations. Mora et al (2021) investigated the joint distribution of three vector-null fields and Voronoï volumes. Other local flow quantities, such as enstrophy (Tagawa et al 2012) and Q-field at particle position (Baker et al 2017), have also been correlated to Voronoï volumes in order to explore the connection with the spatio-temporally evolving vortex structures.…”

“…A recent study by Mora et al. (2021) compares the clustering of three vector nulls, i.e. stagnation points of velocity, Lagrangian acceleration and vorticity, in terms of the scaling properties and dependence.…”