Dissipation range turbulent cascades in plasmas

Terry, P. W.; Almagri, A. F.; Fiksel, G.; Forest, C.B.; Hatch, D. R.; Jenko, F.; Nornberg, M. D.; Prager, S. C.; Ren, Y.; Sarff, J. S.

doi:10.1063/1.3698309

Cited by 18 publications

(28 citation statements)

References 36 publications

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“…Several turbulence models in the literature deviate from this standard picture in that they introduce multiscale forcing and/ or damping with a power-law spectrum, thereby removing the inertial range (in a strict sense) (38)(39)(40). It can be shown, however, that, in general, this modification really affects the system only at very small or very large scales, i.e., in the asymptotic limit (41). If and only if the power-law exponent is such that the linear forcing/ damping rates scale exactly like the nonlinear energy transfer rates, does the forcing/damping affect the entire scale range, inducing nonuniversal behavior (16,42,43).…”

Section: Discussionmentioning

confidence: 97%

New class of turbulence in active fluids

Bratanov

Jenko

Frey

2015

Proc. Natl. Acad. Sci. U.S.A.

151

173

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Turbulence is a fundamental and ubiquitous phenomenon in nature, occurring from astrophysical to biophysical scales. At the same time, it is widely recognized as one of the key unsolved problems in modern physics, representing a paradigmatic example of nonlinear dynamics far from thermodynamic equilibrium. Whereas in the past, most theoretical work in this area has been devoted to NavierStokes flows, there is now a growing awareness of the need to extend the research focus to systems with more general patterns of energy injection and dissipation. These include various types of complex fluids and plasmas, as well as active systems consisting of self-propelled particles, like dense bacterial suspensions. Recently, a continuum model has been proposed for such "living fluids" that is based on the Navier-Stokes equations, but extends them to include some of the most general terms admitted by the symmetry of the problem [Wensink HH, et al. (2012) Proc Natl Acad Sci USA 109:14308-14313]. This introduces a cubic nonlinearity, related to the Toner-Tu theory of flocking, which can interact with the quadratic Navier-Stokes nonlinearity. We show that as a result of the subtle interaction between these two terms, the energy spectra at large spatial scales exhibit power laws that are not universal, but depend on both finite-size effects and physical parameters. Our combined numerical and analytical analysis reveals the origin of this effect and even provides a way to understand it quantitatively. Turbulence in active fluids, characterized by this kind of nonlinear self-organization, defines a new class of turbulent flows.D espite several decades of intensive research, turbulence-the irregular motion of a fluid or plasma-still defies a thorough understanding. It is a paradigmatic example of nonlinear dynamics and self-organization far from thermodynamic equilibrium also closely linked to fundamental questions about irreversibility (1) and mixing (2). The classical example of a turbulent system is a Navier-Stokes flow, with a single quadratic nonlinearity, wellseparated drive and dissipation ranges, and an extended intermediate range of purely conservative scale-to-scale energy transfer (3). However, many turbulent systems of scientific interest involve more general patterns of energy injection, transfer, and dissipation. A fascinating example of these kinds of generalized turbulent dynamics can be observed in dense bacterial suspensions (4). Although the motion of the individual swimmers in the background fluid takes place at Reynolds numbers well below unity, the coarse-grained dynamics of these self-propelled particles display spatiotemporal chaos, i.e., turbulence (5-7). Nevertheless, the correlation functions of the velocity and vorticity fields display some essential differences compared with their counterparts in classical fluid turbulence (8, 9). Moreover, the collective motion of bacteria in such suspensions exhibits long-range correlations (10), appears to be driven by internal instabilities (11), and depends strongly...

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Section: Discussionmentioning

confidence: 97%

New class of turbulence in active fluids

Bratanov

Jenko

Frey

2015

Proc. Natl. Acad. Sci. U.S.A.

151

173

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“…The impact of non-negligible dissipation on the structure of the spectrum has been studied by considering the local energy budget in the k space 21, 22 . We will follow this methodology here, albeit in the context of turbulence with scale-independent anisotropy instead of turbulence that is critically balanced one, as discussed in Section III B.…”

Section: Local Energy Budget In K ⊥ Spacementioning

confidence: 99%

“…Under the local interaction assumption, the local energy budget in the k ⊥ -space naturally arises from considerations of the effective damping and classical resistive diffusion, 21, 22 :…”

Section: Local Energy Budget In K ⊥ Spacementioning

confidence: 99%

“…with p = 6/5 and p = 4/3 in the inviscid and viscous regime respectively, while effective damping coefficient D is given by Eq. (22) and Eq. (23).…”

Section: Local Energy Budget In K ⊥ Spacementioning

confidence: 99%

“…The effective damping caused by the stable modes interrupt the transfer of energy between scales and thus alter the structure of the spectrum. It may then be expected that the resulting spectrum will deviate from the traditional power-law form E (k ⊥ ) ∝ k β 0 ⊥ and take the form of a power law multiplied by an exponential fall E (k ⊥ ) ∝ k β 1 ⊥ exp −δk β 2 ⊥ 21, 22 . Here, β 0 , β 1 , δ and β 2 are constant coefficients.…”

Section: Introductionmentioning

confidence: 99%

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Energy spectrum of tearing mode turbulence in sheared background field

Bhattacharjee

Huang

2018

Physics of Plasmas

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The energy spectrum of tearing mode turbulence in a sheared background magnetic field is studied in this work. We consider the scenario where the nonlinear interaction of overlapping large-scale modes excites a broad spectrum of small-scale modes, generating tearing mode turbulence. The spectrum of such turbulence is of interest since it is relevant to the small-scale back-reaction on the large-scale field. The turbulence we discuss here differs from traditional MHD turbulence mainly in two aspects. One is the existence of many linearly stable small-scale modes which cause an effective damping during energy cascade. The other is the scale-independent anisotropy induced by the large-scale modes tilting the sheared background field, as opposed to the scale-dependent anisotropy frequently encountered in traditional critically balanced turbulence theories. Due to these two differences, the energy spectrum deviates from a simple power law and takes the form of a power law multiplied by an exponential falloff. Numerical simulations are carried out using visco-resistive MHD equations to verify our theoretical predictions, and reasonable agreement is found between the numerical results and our model.

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Kinetic Turbulence

Howes

2014

Astrophysics and Space Science Library

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The weak collisionality typical of turbulence in many diffuse astrophysical plasmas invalidates an MHD description of the turbulent dynamics, motivating the development of a more comprehensive theory of kinetic turbulence. In particular, a kinetic approach is essential for the investigation of the physical mechanisms responsible for the dissipation of astrophysical turbulence and the resulting heating of the plasma. This chapter reviews the limitations of MHD turbulence theory and explains how kinetic considerations may be incorporated to obtain a kinetic theory for astrophysical plasma turbulence. Key questions about the nature of kinetic turbulence that drive current research efforts are identified. A comprehensive model of the kinetic turbulent cascade is presented, with a detailed discussion of each component of the model and a review of supporting and conflicting theoretical, numerical, and observational evidence.

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Dissipation range turbulent cascades in plasmas

Cited by 18 publications

References 36 publications

New class of turbulence in active fluids

New class of turbulence in active fluids

Energy spectrum of tearing mode turbulence in sheared background field

Kinetic Turbulence

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