Anisotropic electrostatic turbulence and zonal flow generation

Balescu, Radu; Petrișor, Iulian; Negrea, Marian

doi:10.1088/0741-3335/47/12/005

Cited by 16 publications

(28 citation statements)

References 12 publications

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“…As future work, it would be worthwhile to carry out a renormalization group analysis of the Leslie's model in the context of earlier work [19][20][21]. It may also be noted that an approach similar to that presented here can be applied to other physical problems such as zonal flow generation in an anisotropic turbulence regime [22].…”

Section: Discussionmentioning

confidence: 91%

A rigorous framework for Leslie's model of homogeneous anisotropic turbulence

Nandy¹

2007

J. Phys. A: Math. Theor.

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Leslie, in the book Developments in the Theory of Turbulence (1973 Oxford: Clarendon), offered a very simple and intuitively founded model for the case of homogeneous anisotropic turbulence. Here, we offer a rigorous reformulation of Leslie's model leading to a general form for the velocity correlation tensor that satisfies realizability conditions like symmetry in its tensor indices and the condition of solenoidality arising from the incompressibility condition. The anisotropic part of the correlation tensor involves two non-dimensional constants-one arising from the pure strain term and the other from the term that induces distortion in the wave vector space; the rapid pressure term does not contribute. The estimates for these non-dimensional constants yield encouraging results within this framework.

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Section: Discussionmentioning

confidence: 91%

A rigorous framework for Leslie's model of homogeneous anisotropic turbulence

Nandy¹

2007

J. Phys. A: Math. Theor.

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“…In the same spirit, it would also be interesting to study other integro-differential closures, possibly including turbulent systems with spectra varying in both the wave number and the physical space, e.g. non-Markovian Liouville equation suggested in references [34,35] for the plasma drift waves.…”

Section: Discussionmentioning

confidence: 99%

Inverse cascade anomalies in fourth-order Leith models

Thalabard¹,

Медведев²,

Grebenev³

et al. 2021

J. Phys. A: Math. Theor.

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We analyze a family of fourth-order non-linear diffusion models corresponding to local approximations of 4-wave kinetic equations of weak wave turbulence. We focus on a class of parameters for which a dual cascade behaviour is expected with an infrared finite-time singularity associated to inverse transfer of waveaction. This case is relevant for wave turbulence arising in the Nonlinear Schrödinger model and for the gravitational waves in the Einstein’s vacuum field model. We show that inverse transfer is not described by a scaling of the constant-flux solution but has an anomalous scaling. We compute the anomalous exponents and analyze their origin using the theory of dynamical systems.

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“…Various aspects of the transport in fusion plasmas were studied using the DTM, that was developed and adapted to the study of models with increased complexity [32][33][34][35][36][37][38][39][40].…”

Section: Trapping and Micro-confinement Description By Dtmmentioning

confidence: 99%

Random and quasi-coherent aspects in particle motion and their effects on transport and turbulence evolution

Vlad

Spineanu

2017

New J. Phys.

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The quasi-coherent effects in two-dimensional incompressible turbulence are analyzed starting from the test particle trajectories. They can acquire coherent aspects when the stochastic potential has slow time variation and the motion is not strongly perturbed. The trajectories are, in these conditions, random sequences of large jumps and trapping or eddying events. Trapping determines quasicoherent trajectory structures, which have a micro-confinement effect that is reflected in the transport coefficients. They determine non-Gaussian statistics and flows associated to an average velocity. Trajectory structures also influence the test modes on turbulent plasmas. Nonlinear damping and generation of zonal flow modes is found in drift turbulence in uniform magnetic field. The coupling of test particle and test mode studies permitted to evaluate the self-consistent evolution of the drift turbulence in an iterated approach. The results show an important nonlinear effect of ion diffusion, which can prevent the transition to the nonlinear regime at small drive of the instability. At larger drive, quasi-coherent trajectory structures appear and they have complex effects on turbulence.eddying. The general conclusion of these studies is that trajectory trapping or eddying determines non-standard statistics of trajectories: non-Gaussian distributions, long time Lagrangian correlations (memory), strongly modified transport coefficients and an increased degree of coherence. The trapped trajectories form quasicoherent structures similar to fluid vortices.Very recent results [15] have shown that these methods could be the basis for the development of a theoretical approach for the study of test modes in turbulent plasmas. It is similar to the Lagrangian approach initiated by Dupree [16,17] and developed in the 1970s. The assumption of random trajectories with Gaussian distribution limited the application of Dupree's method to the quasilinear regime. The DTM and NSA enable the evaluation of the average propagator of the test modes in the nonlinear regime and extend the theoretical procedure to the complex processes that are generated in these conditions. The tendency of drift turbulence evolution beyond the quasilinear regime was obtained in [15].We present a theoretical approach to the study of turbulence evolution, the iterated self-consistent method (ISC). It is based on the analysis of the test particles and test modes in turbulent plasmas. Both test particle and test mode studies start from given statistical description of the turbulence. However, the coupling of these problems can lead to the evaluation of turbulence evolution and to the understanding of the nonlinear processes that are generated. The ISC is applied here to the drift turbulence in plasmas confined in uniform magnetic fields.The paper is organized as follows. The physical processes analyzed in this paper and the main ideas that are followed in this study are presented in section 2. Section 3 contains the test particle studies of transport, the DTM and the NS...

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Anisotropic electrostatic turbulence and zonal flow generation

Cited by 16 publications

References 12 publications

A rigorous framework for Leslie's model of homogeneous anisotropic turbulence

A rigorous framework for Leslie's model of homogeneous anisotropic turbulence

Inverse cascade anomalies in fourth-order Leith models

Random and quasi-coherent aspects in particle motion and their effects on transport and turbulence evolution

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