Revisiting a Classic: The Parker–moffatt Problem

Pezzi, Oreste; Parashar, T. N.; Servidio, S.; Valentini, F.; Vásconez, Christian L.; Yang, Yan; Malara, F.; Matthaeus, W. H.; Veltri, P.

doi:10.3847/1538-4357/834/2/166

Cited by 37 publications

(20 citation statements)

References 43 publications

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“…The results of the gyrokinetic simulation of strong Alfvén wavepacket collisions presented here, however, stand in stark contrast to the results of the study by Pezzi et al (2017), which finds that after the collision, in both their compressible MHD and Hybrid Vlasov-Maxwell simulations, the wavepackets do not separate cleanly and continue to evolve, as illustrated in Figure 1 of their paper. What is the cause for the dramatic contradiction in these results?…”

Section: Relation To Similar Wavepacket Collision Simulationscontrasting

confidence: 99%

“…We argue here that the limitation of the Pezzi et al. (2017) simulations to two spatial dimensions is the root of these striking differences. Due to the large computational cost of running the Hybrid Vlasov–Maxwell (HVM) code (Valentini et al.…”

Section: Evolution Of the Nonlinear Interactionmentioning

confidence: 64%

“…A recent study by Pezzi et al. (2017) has used numerical simulations to tackle what they term the ‘Parker–Moffatt problem.’ The basic question is inspired by the properties of incompressible MHD equations given in § 3.1: do two initially separated, localized Alfvén wavepackets interact nonlinearly only during the time that they overlap, and then cease evolving after they have passed through each other and become separated again? The simulation results shown in figure 2, and examined in further detail in the subsections above, definitively answer this question – yes.…”

Section: Evolution Of the Nonlinear Interactionmentioning

confidence: 99%

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Nonlinear energy transfer and current sheet development in localized Alfvén wavepacket collisions in the strong turbulence limit

2018

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In space and astrophysical plasmas, turbulence is responsible for transferring energy from large scales driven by violent events or instabilities, to smaller scales where turbulent energy is ultimately converted into plasma heat by dissipative mechanisms. The nonlinear interaction between counterpropagating Alfvén waves, denoted Alfvén wave collisions, drives this turbulent energy cascade, as recognized by early work with incompressible magnetohydrodynamic (MHD) equations. Recent work employing analytical calculations and nonlinear gyrokinetic simulations of Alfvén wave collisions in an idealized periodic initial state have demonstrated the key properties that strong Alfvén wave collisions mediate effectively the transfer of energy to smaller perpendicular scales and self-consistently generate current sheets. For the more realistic case of the collision between two initially separated Alfvén wavepackets, we use a nonlinear gyrokinetic simulation to show here that these key properties persist: strong Alfvén wavepacket collisions indeed facilitate the perpendicular cascade of energy and give rise to current sheets. Furthermore, the evolution shows that nonlinear interactions occur only while the wavepackets overlap, followed by a clean separation of the wavepackets with straight uniform magnetic fields and the cessation of nonlinear evolution in between collisions, even in the gyrokinetic simulation presented here which resolves dispersive and kinetic effects beyond the reach of the MHD theory.

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Section: Relation To Similar Wavepacket Collision Simulationscontrasting

confidence: 99%

Section: Evolution Of the Nonlinear Interactionmentioning

confidence: 64%

Section: Evolution Of the Nonlinear Interactionmentioning

confidence: 99%

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Nonlinear energy transfer and current sheet development in localized Alfvén wavepacket collisions in the strong turbulence limit

2018

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“…The interaction of two waves has been studied analytically [Howes and Nielson, 2013], numerically [Pezzi et al, 2017a[Pezzi et al, , 2017b, and even in a laboratory [Howes et al, 2012b]. Three wave interactions satisfy the frequency 1 + 2 = 3 and wave vector equations k 1 + k 2 = k 3 .…”

Section: Discussionmentioning

confidence: 99%

Multipoint analysis of compressive fluctuations in the fast and slow solar wind

Roberts,

Narita,

et al. 2017

JGR Space Physics

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Compressible turbulence in the solar wind is a topic of much recent debate. To understand the various compressive fluctuations at scales comparable to proton characteristic lengths, we use multipoint magnetic field and density data (derived from spacecraft potential which allows higher time resolution than is typically possible than with particle instruments) from the Cluster spacecraft when they were in undisturbed intervals of slow and fast solar wind. The application of the multipoint signal resonator technique is performed for the first time, to the analysis of scalar time series. Fluctuations in the measurements of electron density and in magnitude of the magnetic field (used as a proxy for compressible magnetic fluctuations) are used as inputs in addition to the traditional vector components of the magnetic field. This analysis is performed on two streams of solar wind, one which can be classed as a slow stream and one which can be classed as a fast stream to investigate the difference in the compressible components in the two types of wind. The recovered plasma frame frequencies for the incompressible component show low propagation speed in the plasma frame consistent with previous applications of the method, while the compressible components are more scattered, some with very high phase speeds. Based on these results, we propose a picture of compressive solar wind turbulence as a mixed state of (1) linear modes such as kinetic Alfvén, kinetic slow, and ion Bernstein modes; (2) coherent structures with very small intrinsic frequencies; and (3) nonlinear or sideband modes.

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“…Several different schemes have been employed including magnetohydrodynamic (MHD) at large scales (e.g. Verdini and Grappin, 2015;Mallet et al, 2016;Pezzi et al, 2017a;Pezzi et al, 2017b), Hall MHD for scales at the transition between proton and electron scales (Pucci et al, 2016;Pezzi et al, 2017a;Pezzi et al, 2017b), hybrid Vlasov (e.g. Perrone et al, 2013;Franci et al, 2015a, b;Valentini et al, 2016;Cerri et al, 2016Cerri et al, , 2017Pezzi et al, 2017a;Pezzi et al, 2017b) or hybrid particle in cell for proton kinetic scales, finally full particle in cell descriptions can be used to investigate sub-ion scales (Camporeale and Burgess, 2011;Haynes et al, 2014; see also the review by Servidio et al, 2014).…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional density and compressible magnetic structure in solar wind turbulence

2018

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Abstract. The three-dimensional structure of both compressible and incompressible components of turbulence is investigated at proton characteristic scales in the solar wind. Measurements of the three-dimensional structure are typically difficult, since the majority of measurements are performed by a single spacecraft. However, the Cluster mission consisting of four spacecraft in a tetrahedral formation allows for a fully three-dimensional investigation of turbulence. Incompressible turbulence is investigated by using the three vector components of the magnetic field. Meanwhile compressible turbulence is investigated by considering the magnitude of the magnetic field as a proxy for the compressible fluctuations and electron density data deduced from spacecraft potential. Application of the multi-point signal resonator technique to intervals of fast and slow wind shows that both compressible and incompressible turbulence are anisotropic with respect to the mean magnetic field direction P ⊥ P and are sensitive to the value of the plasma beta (β; ratio of thermal to magnetic pressure) and the wind type. Moreover, the incompressible fluctuations of the fast and slow solar wind are revealed to be different with enhancements along the background magnetic field direction present in the fast wind intervals. The differences in the fast and slow wind and the implications for the presence of different wave modes in the plasma are discussed.

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Revisiting a Classic: The Parker–moffatt Problem

Cited by 37 publications

References 43 publications

Nonlinear energy transfer and current sheet development in localized Alfvén wavepacket collisions in the strong turbulence limit

Nonlinear energy transfer and current sheet development in localized Alfvén wavepacket collisions in the strong turbulence limit

Multipoint analysis of compressive fluctuations in the fast and slow solar wind

Three-dimensional density and compressible magnetic structure in solar wind turbulence

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