Triad interactions and the bidirectional turbulent cascade of magnetic helicity

Linkmann, Moritz; Dallas, Vassilios

doi:10.1103/physrevfluids.2.054605

Cited by 10 publications

(15 citation statements)

References 41 publications

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“…The observed dynamics is qualitatively similar to that obtained in numerical simulations of EMHD (Kim & Cho 2015) and also of incompressible MHD in the absence of an ambient field (Müller et al. 2012; Linkmann & Dallas 2017). At the final time of the simulation, the energy has almost reached the lowest modes and a separate simulation is needed to address the situation where the cascade crosses and penetrates into the weakly dispersive range.…”

Section: Global Properties Of the Gch Inverse Cascadesupporting

confidence: 83%

“…In this context, special attention has been paid in the literature to the cascade of magnetic helicity in the framework of incompressible magnetohydrodynamics (MHD) in the absence of an ambient field (Frisch et al. 1975; Pouquet, Frisch & Leorat 1976; Meneguzzi, Frisch & Pouquet 1981; Alexakis, Mininni & Pouquet 2006; Müller, Malapaka & Busse 2012; Linkmann & Dallas 2016, 2017; Pouquet et al. 2019).…”

Section: Introductionmentioning

confidence: 99%

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Inverse cascade and magnetic vortices in kinetic Alfvén-wave turbulence

et al. 2021

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A Hamiltonian two-field gyrofluid model for kinetic Alfvén waves (KAWs) in a magnetized electron–proton plasma, retaining ion finite-Larmor-radius corrections and parallel magnetic field fluctuations, is used to study the inverse cascades that develop when turbulence is randomly driven at sub-ion scales. In the directions perpendicular to the ambient field, the dynamics of the cascade turns out to be non-local and the ratio $\chi _f$ of the wave period to the characteristic nonlinear time at the driving scale affects some of its properties. For example, at small values of $\chi _f$ , parametric decay instability of the modes driven by the forcing can develop, enhancing for a while inverse transfers. The balanced state, obtained at early time when the two counter-propagating waves are equally driven, also becomes unstable at small $\chi _f$ , leading to an inverse cascade. For $\beta _e$ smaller than a few units, the cascade slows down when reaching the low-dispersion spectral range. For higher $\beta _e$ , the ratio of the KAW to the Alfvén frequencies displays a local minimum. At the corresponding transverse wavenumber, a condensate is formed, and the cascade towards larger scales is then inhibited. Depending on the parameters, a parallel inverse cascade can develop, enhancing the elongation of the ion-scale magnetic vortices that generically form.

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Section: Global Properties Of the Gch Inverse Cascadesupporting

confidence: 83%

Section: Introductionmentioning

confidence: 99%

Inverse cascade and magnetic vortices in kinetic Alfvén-wave turbulence

et al. 2021

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“…The figure here is a simple illustration of the phenomenon. Detailed triadic interactions of such an inverse cascade are studied in Linkmann et al () and Linkmann and Dallas () using a classical helical decomposition, with both analytical and numerical tools at resolutions of 512 3 points. These authors show in particular that the relative signs of kinetic and magnetic helicity play a direct role in the emergence of large‐scale dynamo fields, with growth rates that are determined in the ideal (nondissipative) case and thus independent of the magnitude of the magnetic Reynolds number, with no subsequent so‐called α quenching (see also Pouquet et al, ).…”

Section: Coupling To a Magnetic Fieldmentioning

confidence: 99%

Helicity Dynamics, Inverse, and Bidirectional Cascades in Fluid and Magnetohydrodynamic Turbulence: A Brief Review

Pouquet

Rosenberg

Stawarz

et al. 2019

Earth and Space Science

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We briefly review helicity dynamics, inverse and bidirectional cascades in fluid and magnetohydrodynamic (MHD) turbulence, with an emphasis on the latter. The energy of a turbulent system, an invariant in the nondissipative case, is transferred to small scales through nonlinear mode coupling. Fifty years ago, it was realized that, for a two‐dimensional fluid, energy cascades instead to larger scales and so does magnetic excitation in MHD. However, evidence obtained recently indicates that, in fact, for a range of governing parameters, there are systems for which their ideal invariants can be transferred, with constant fluxes, to both the large scales and the small scales, as for MHD or rotating stratified flows, in the latter case including quasi‐geostrophic forcing. Such bidirectional, split, cascades directly affect the rate at which mixing and dissipation occur in these flows in which nonlinear eddies interact with fast waves with anisotropic dispersion laws, due, for example, to imposed rotation, stratification, or uniform magnetic fields. The directions of cascades can be obtained in some cases through the use of phenomenological arguments, one of which we derive here following classical lines in the case of the inverse magnetic helicity cascade in electron MHD. With more highly resolved data sets stemming from large laboratory experiments, high‐performance computing, and in situ satellite observations, machine learning tools are bringing novel perspectives to turbulence research. Such algorithms help devise new explicit subgrid‐scale parameterizations, which in turn may lead to enhanced physical insight, including in the future in the case of these new bidirectional cascades.

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“…Nevertheless, we must bear in mind that a large network of triadic interactions as in the Navier-Stokes equations can evolve differently than a set of isolated triads, as previously pointed out in Refs. [15,16].…”

Section: Introductionmentioning

confidence: 99%

Regime transition in the energy cascade of rotating turbulence

Pestana

Hickel

2019

Phys. Rev. E

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Transition from a split to a forward kinetic energy cascade system is explored in the context of rotating turbulence using direct numerical simulations with a three-dimensional isotropic random force uncorrelated with the velocity field. Our parametric study covers confinement effects in large aspect ratio domains and a broad range of rotation rates. The data here presented add substantially to previous works, which, in contrast, focused on smaller and shallower domains. Results indicate that for fixed geometrical dimensions the Rossby number acts as a control parameter, whereas for a fixed Rossby number the product of the domain size along the rotation axis and forcing wavenumber governs the amount of energy that cascades inversely. The regime transition criterion hence depends on both control parameters.

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Triad interactions and the bidirectional turbulent cascade of magnetic helicity

Cited by 10 publications

References 41 publications

Inverse cascade and magnetic vortices in kinetic Alfvén-wave turbulence

Inverse cascade and magnetic vortices in kinetic Alfvén-wave turbulence

Helicity Dynamics, Inverse, and Bidirectional Cascades in Fluid and Magnetohydrodynamic Turbulence: A Brief Review

Regime transition in the energy cascade of rotating turbulence

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