Lagrangian versus Eulerian correlations and transport scaling

Abstract

The effect of the shape of the Eulerian correlation of an electrostatic turbulence on the scaling of the diffusion coefficient is studied using the decorrelation trajectory method. We show that a strong influence appears due to trajectory trapping when the Kubo number is larger than 1.

Turbulent E×B advection of charged test particles with large gyroradii

“…This is in line with the finding that a more moderate decay of the autocorrelation in space leads to a slower reduction of the diffusion coefficient for large and growing Kubo numbers. [5] Due to this widening effect, the curves for different gyroradii in Fig. 1 are actually able to intersect.…”

“…Second, due to the factorization of space and time correlations, it is possible to relate the two quantities D(t, K → ∞) and D(t → ∞, K) to each other as is shown in Ref. [5]. In other words, the long-time limit of the diffusivity for different Kubo numbers can be computed from the timedependent diffusivity in a static potential.…”

“…[4,5] Recently, the DCT approach has been applied to the E×B drift motion of ions with large gyroradii, yielding very surprising and counterintuitive results. [2,3] The goal of this section is to briefly review the DCT theory, in particular in relation to the latter problem, thus providing a starting point for a modified DCT approach which will be presented and discussed in the next section.…”

“…In other words, the time dependent diffusion coefficient D x (t) is the time integral over the Lagrangian correlation function L xx (t) of the particle's drift velocity. The DCT method developed by M. Vlad and co-workers [4,5,2,3] offers a possibility to calculate the Lagrangian correlation function from the corresponding Eulerian correlation function. Here, in contrast to previous attempts to connect these two types of correlations, particle trapping effects are retained.…”

“…The present work was inspired, in part, by two recent papers by M. Vlad and co-workers [2,3] in which they extended the so-called decorrelation trajectory (DCT) method [4,5] for computing diffusivities from the autocorrelation function of the potential to the case of particles with finite gyroradii. And the results they got were very surprising.…”