Lagrangian particle statistics in turbulent flows from a simple vortex model

Abstract

The statistics of Lagrangian particles in turbulent flows is considered in the framework of a simple vortex model. Here, the turbulent velocity field is represented by a temporal sequence of Burgers vortices of different circulation, strain, and orientation. Based on suitable assumptions about the vortices' statistical properties, the statistics of the velocity increments is derived. In particular, the origin and nature of small-scale intermittency in this model is investigated both numerically and analytically. We critically compare our results to experimental studies.

On small-scale and large-scale intermittency of Lagrangian statistics in canopy flow

“…In addition to that, for the components’ increments were anti-correlated, which, as shown by Wilczek et al. (2008), can result from trajectories rotation around vortex filaments’ cores; this too supports the picture of vortex trapping. Thus, figure 3( b ) supports the notion that small-scale Lagrangian intermittency in the canopy flow is related to the encounter of trajectories with sparse and intense vortex filaments, similar to the HIT case.…”

“…Let us briefly consider dynamical scenarios for small-scale Lagrangian intermittency. Results from HIT DNS by Biferale et al (2005), Bec et al (2006) and Bentkamp et al (2019) suggested that small-scale intermittency is a result of encounters between particles and intense vortex filaments; indeed, Wilczek, Jenko & Friedrich (2008) showed that the characteristic transition of the increments' p.d.f.s can be captured by a heuristic flow model of superimposed constitutive vortices. Similarly, Liberzon et al (2012) showed that acceleration-vorticity-strain alignment in a quasi-homogeneous flow is associated with intense energy flux.…”

Turbulent transport with intermittency: Expectation of a scalar concentration

“…Specific turbulent flow structures, vortices [e.g. [10][11][12] and straining stagnation points [13,14], have been identified as likely important to the statistics of those motions, and both of these have been employed as fundamental dynamical components in models of Lagrangian velocity increments [15][16][17] and pair dispersion [18][19][20][21].…”

Understanding droplet collisions through a model flow: Insights from a Burgers vortex

“…Moreover, ensembles of such model vortices have been shown to provide a reasonable approximation, and hence a testing ground, for realistic turbulent flows [35]. This has motivated earlier authors to use such models for understanding problems of Lagrangian turbulence [36] as well as turbulent transport of heavy inertial particles [37,38]. In a similar spirit, we analyze the relative motion of droplets suspended in and around a Burgers vortex, in order to gain insight into the enhancement of droplet collisions by intense vortical structures in turbulent flows.…”