Cascades and Dissipative Anomalies in Compressible Fluid Turbulence

Eyink, Gregory L.; Drivas, Theodore D.

doi:10.1103/physrevx.8.011022

Cited by 61 publications

(93 citation statements)

References 120 publications

(314 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Collisions act in the phase-space cascade, dissipating enstrophy at the finest scales (thus increasing plasma entropy), similarly to Navier-Stokes turbulence. Similarly to the termination of the cascade in classical fluids, where energy is cancelled by viscous terms at small spatial scales, here we observe that the collisional operator acts at large values of m, effectively damping the enstrophy cascade Eyink 2018). As it can be seen, the rollover of spectra occurs at m ∼ 40 in the collisionless case and at m ∼ 20 for the collisional run.…”

Section: Discussionsupporting

confidence: 67%

“…To further point out how collisions affect the presence of non-thermal features in the proton VDF, in this section we investigate the development of a phase-space cascade, which is induced by the presence of turbulent fluctuations, as recently proposed in several works Servidio et al 2017;Cerri, Kunz & Califano 2018;Pezzi et al 2018a;Eyink 2018). The idea of this process is that collisionless plasma turbulence initiates the production of a cascade-like process in the full phase-space, leading to the formation of non-Maxwellian features.…”

Section: Phase-space Enstrophy Cascadementioning

confidence: 97%

See 1 more Smart Citation

Proton–Proton Collisions in the Turbulent Solar Wind: Hybrid Boltzmann–Maxwell Simulations

Pezzi

Perrone

Servidio

et al. 2019

ApJ

View full text Add to dashboard Cite

The mechanism of heating for hot, dilute and turbulent plasmas represents a longstanding problem in space physics, whose implications concern both near-Earth environments and astrophysical systems. n order to explore the possible role of inter-particle collisions, simulations of plasma turbulence -in both collisionless and collisional regimehave been compared by adopting Eulerian Hybrid Boltzmann-Maxwell simulations, being proton-proton collisions explicitly introduced through the nonlinear Dougherty operator. Although collisions do not significantly influence the statistical characteristics of the turbulence, they dissipate non-thermal features in the proton distribution function and suppress the enstrophy/entropy cascade in the velocity space, damping the spectral transfer towards large Hermite modes. This enstrophy dissipation is particularly effective in regions where the plasma distribution function is strongly distorted, suggesting that collisional effects are enhanced by fine velocity-space structures. A qualitative connection between the turbulent energy cascade in fluids and the enstrophy cascade in plasmas has been established, opening a new path on the understanding of astrophysical plasma turbulence.

show abstract

Section: Discussionsupporting

confidence: 67%

Section: Phase-space Enstrophy Cascadementioning

confidence: 97%

Proton–Proton Collisions in the Turbulent Solar Wind: Hybrid Boltzmann–Maxwell Simulations

Pezzi

Perrone

Servidio

et al. 2019

ApJ

View full text Add to dashboard Cite

show abstract

“…This condition can be restated as η where η is the resistive dissipation length specified by η δv( η ) η. Similar conditions guarantee validity of all of the other ideal equations as well (see Eyink and Drivas, 2018).…”

Section: B Renormalization Of Mhd Equations and Singularitiesmentioning

confidence: 69%

“…Extending Onsager's analysis to MHD plasmas, turbulent solutions are found to suffer several dissipative anomalies which require diverging gradients of all MHD fields, e.g., velocity field, magnetic field, density etc. (see e.g., Mininni and Pouquet (2009) ;Caflisch, Klapper, and Steele (1997); Eyink and Drivas (2018). For example, magnetic-field gradients blow up in the limit as magnetic diffusivity η tends to zero, with ∇B → ∞ as η → 0.…”

Section: A Spontaneous Stochasticitymentioning

confidence: 99%

3D turbulent reconnection: Theory, tests, and astrophysical implications

Lazarían¹,

et al. 2020

Self Cite

View full text Add to dashboard Cite

Magnetic reconnection, topological change in magnetic fields, is a fundamental process in magnetized plasmas. It is associated with energy release in regions of magnetic field annihilation, but this is only one facet of this process. Astrophysical fluid flows normally have very large Reynolds numbers and are expected to be turbulent, in agreement with observations. In strong turbulence magnetic field lines constantly reconnect everywhere and on all scales, thus making magnetic reconnection an intrinsic part of the turbulent cascade. We note in particular that this is inconsistent with the usual practice of regarding magnetic field lines as persistent dynamical elements. A number of theoretical, numerical, and observational studies starting with the Lazarian & Vishniac 1999 paper proposed that 3D turbulence makes magnetic reconnection fast and that magnetic reconnection and turbulence are intrinsically connected. In particular, we discuss the dramatic violation of the textbook concept of magnetic flux-freezing in the presence of turbulence. We demonstrate that in the presence of turbulence the plasma effects are subdominant to turbulence as far as the magnetic reconnection is concerned. The latter fact justifies an MHD-like treatment of magnetic reconnection on all scales much larger than the relevant plasma scales. We discuss numerical and observational evidence supporting the turbulent reconnection model. In particular, we demonstrate that the tearing reconnection is suppressed in 3D and, unlike the 2D settings, 3D reconnection induces turbulence that makes magnetic reconnection independent of resistivity. We show that turbulent reconnection dramatically affects key astrophysical processes, e.g. star formation, turbulent dynamo, acceleration of cosmic rays. We provide criticism of the concept of "reconnection-mediated turbulence" and explain why turbulent reconnection is very different from enhanced turbulent resistivity and hyper-resistivity, and why the latter have fatal conceptual flaws.

show abstract

“…where c s is constant, presents high interest because of its astrophysical applications, see e. g. [10] and cf. [37]. In this case the equations are invariant with respect to rescaling of the density by a constant, cf.…”

Section: Fundamentalsmentioning

confidence: 99%

Density and tracer statistics in compressible turbulence: Phase transition to multifractality

Fouxon

Mond

2019

Phys. Rev. E

View full text Add to dashboard Cite

We study the statistics of fluid (gas) density and concentration of passive tracer particles (dust) in compressible turbulence. We raise the question of whether the fluid density which is an active field that reacts back on the transporting flow and the passive concentration of tracers must coincide in the steady state, which we demonstrate to be crucial both theoretically and experimentally. The fields' coincidence is provable at small Mach numbers, however at finite Mach numbers the assumption of mixing is needed which we demonstrate to be not self-evident due to the possibility of self-organization. Irrespective of whether the fields coincide we obtain a number of rigorous conclusions on both fields. As Ma increases from small or moderate values the density and the concentration in the inertial range go through a phase transition from a finite continuous smooth to a singular multifractal spatial distribution. The concept of sum of Lyapunov exponents in the multifractal phase is generalizable to the inertial range implying a singular tracers' distribution. We discuss various concepts of multifractality and propose a way to calculate fractal dimensions from numerical or experimental data. We derive a simple expression for the spectrum of fractal dimensions of isothermal turbulence and describe limitations of lognormality. The expression depends on a single parameter: the scaling exponent of the density spectrum. We propose a mechanism for the phase transition of concentration to multifractality. We demonstrate that the pair-correlation function is invariant under the action of the probability density function of the inter-pair distance that has the Markov property. This implies applicability of the compressible version of the Kraichnan turbulence model. We use the model to derive an explicit expression for the tracers pair correlation that demonstrates their smooth transition to multifractality and confirms the transition's mechanism. The obtained fractal dimension explains previous numerical observations. Our results are of potentially important implications on astrophysical problems such as star formation as well as on technological applications such as supersonic combustion. As an example we demonstrate strong increase of planetesimals formation rate at the transition.

show abstract

Cascades and Dissipative Anomalies in Compressible Fluid Turbulence

Cited by 61 publications

References 120 publications

Proton–Proton Collisions in the Turbulent Solar Wind: Hybrid Boltzmann–Maxwell Simulations

Proton–Proton Collisions in the Turbulent Solar Wind: Hybrid Boltzmann–Maxwell Simulations

3D turbulent reconnection: Theory, tests, and astrophysical implications

Density and tracer statistics in compressible turbulence: Phase transition to multifractality

Contact Info

Product

Resources

About