Trajectory statistics and turbulence evolution

Abstract

The aim of this paper is to understand the tendency to organization of the turbulence in two-dimensional ideal fluids. We show that nonlinear processes as inverse cascade of the energy and vorticity concentration are essentially determined by trajectory trapping or eddying. The statistics of the trajectories of the vorticity elements is studied using a semianalytic method. The separation of the positive and negative vorticity is due to the attraction produced by a large scale vortex on the small scale vortices of the same sign. More precisely, a large scale velocity is shown to determine average transverse drifts, which have opposite orientations for positive and negative vorticity. They appear in the presence of trapping and lead to energy flow to large scales due to the increase of the circulation of the large vortex. Recent results on drift turbulence evolution in magnetically confined plasmas are discussed in order to underline the idea that there is a link between the inverse cascade and trajectory trapping. The physical mechanisms are different in fluids and plasmas due to the different types of nonlinearities of the two systems, but trajectory trapping has the main role in both cases.

Contributions of plasma physics to chaos and nonlinear dynamics

“…This yields the decorrelation trajectory method (Vlad, Spineanu, Misguich & Balescu 1998) and the nested subensemble approach (Vlad et al 2004). These techniques are extensively used for the study of the transport in magnetically confined plasmas (see (Vlad & Spineanu 2013) for a recent set of references), and for the study of astrophysical plasmas (Vlad & Spineanu 2014) and of fluids (Vlad & Spineanu 2015). Reference (Vlad et al 1998) computes numerically the diffusion coefficient of particles in a spectum of waves scaling like k −3 , and for Kubo numbers up to 210 5 .…”

Quasi-coherent structures and flows in turbulent transport

“…The detailed effective calculations are presented in [6][7][8]. Applications of the DTM for more complicated transport processes can be found in [14]- [19] for plasma turbulence and in [20]- [21] for space plasmas.…”

“…The parameters of the quasi-coherent structures are determined using the DTM as time dependent functions [14]. The fraction of trapped trajectories ntr(t) counts the number of trajectories that are closed at time t in a frozen potential.…”

The emergence of self-organization in complex systems–Preface

“…In these systems complexity is intimately connected with some physical properties that are heterogeneously distributed, even if, in some applications, the medium can be considered statistically homogeneous (see paper [20]). The authors of paper [18] discuss the self-organizing character of two-dimensional turbulence by using a stochastic Lagrangian approach. They show that self-organization is associated with trajectory trapping, being a typical particle trajectory characterized by a random sequence of long (non-Gaussian) jumps and trapping events.…”

“…Papers [18,19,20,21,22,23] are mainly devoted to anomalous transport in complex media and complex materials, from complex fluids to porous media. In these systems complexity is intimately connected with some physical properties that are heterogeneously distributed, even if, in some applications, the medium can be considered statistically homogeneous (see paper [20]).…”