Inertial/kinetic-Alfvén wave turbulence: A twin problem in the limit of local interactions

Galtier, Sébastien; David, Vincent

doi:10.1103/physrevfluids.5.044603

Cited by 11 publications

(7 citation statements)

References 55 publications

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“…It is also due to the helical nature of the waves. This reinforces the bridge between plasma physics and fluid mechanics (see also Galtier & David 2020) and suggests that laboratory experiments (Yarom & Sharon 2014;Monsalve et al 2020) can help to better understand space plasma physics at a scale still difficult to detect by current spacecraft.…”

Section: Discussionsupporting

confidence: 66%

“…It is interesting to note that a similar nonlinear diffusion equation has been obtained, in the same approximation of wave turbulence, for EMHD (David & Galtier 2019; Passot & Sulem 2019) and rotating hydrodynamics (Galtier & David 2020). The numerical simulations of this equation reveal the existence of a energy spectrum during the non-stationary phase that is steeper than the KZ spectrum.…”

Section: Super-local Interactionsmentioning

confidence: 57%

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Wave turbulence in inertial electron magnetohydrodynamics

David

Galtier

2022

J. Plasma Phys.

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A wave turbulence theory is developed for inertial electron magnetohydrodynamics (IEMHD) in the presence of a relatively strong and uniform external magnetic field $\boldsymbol {B_0} = B_0 \hat {\boldsymbol {e}}_\|$ . This regime is relevant for scales smaller than the electron inertial length $d_e$ . We derive the kinetic equations that describe the three-wave interactions between inertial whistler or kinetic Alfvén waves. We show that for both invariants, energy and momentum, the transfer is anisotropic (axisymmetric) with a direct cascade mainly in the direction perpendicular ( $\perp$ ) to $\boldsymbol {B_0}$ . The exact stationary solutions (Kolmogorov–Zakharov spectra) are obtained for which we prove the locality. We also found the Kolmogorov constant $C_K \simeq 8.474$ . In the simplest case, the study reveals an energy spectrum in $k_\perp ^{-5/2} k_\|^{-1/2}$ (with k the wavenumber) and a momentum spectrum enslaved to the energy dynamics in $k_\perp ^{-3/2} k_\|^{-1/2}$ . These solutions correspond to a magnetic energy spectrum ${\sim }k_\perp ^{-9/2}$ , which is steeper than the EMHD prediction made for scales larger than $d_e$ . We conclude with a discussion on the application of the theory to space plasmas.

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Section: Discussionsupporting

confidence: 66%

Section: Super-local Interactionsmentioning

confidence: 57%

Wave turbulence in inertial electron magnetohydrodynamics

David

Galtier

2022

J. Plasma Phys.

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“…The locality of the KZ spectrum gives some support to the limit of super-local interactions sometimes taken to simplify the study of wave turbulence. Under this limit, a nonlinear diffusion equation is found analytically with which the numerical study becomes much easier (Galtier & David 2020). Interestingly, it was shown with this model that the non-stationary solution exhibits a spectrum, which is understood as a self-similar solution of the second kind, before forming – as expected – the KZ stationary spectrum after a bounce at small scales.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Locality of triad interaction and Kolmogorov constant in inertial wave turbulence

David

Galtier

2023

J. Fluid Mech.

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Using the theory of wave turbulence for rapidly rotating incompressible fluids derived by Galtier (Phys. Rev. E, vol. 68, 2003, 015301), we find the locality conditions that the solutions of the kinetic equation must satisfy. We show that the exact anisotropic Kolmogorov–Zakharov spectrum satisfies these conditions, which justifies the existence of this constant (positive) energy flux solution. Although a direct cascade is predicted in the transverse ( $\perp$ ) and parallel ( $\parallel$ ) directions to the rotation axis, we show numerically that in the latter case some triadic interactions can have a negative contribution to the energy flux, while in the former case all interactions contribute to a positive flux. Neglecting the parallel energy flux, we estimate the Kolmogorov constant at $C_K \simeq 0.749$ . These results provide theoretical support for recent numerical and experimental studies.

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“…The concepts developed here would allow us to revisit certain physical phenomena such as turbulence, where rotation and incessant changes in the trajectory of the fluid play decisive roles in energy transfers between vortices. The particular case of turbulence in rotating flows is very prominent in the literature and applications [9,4,3,8]; the influence of the formulation of inertial terms could be studied on cases already treated.…”

Section: Introductionmentioning

confidence: 99%

On Helmholtz–Hodge decomposition of inertia on a discrete local frame of reference

Caltagirone

2020

Physics of Fluids

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The notion of inertial reference frame is abandoned and I replaced it by a local reference frame on which the fundamental law of mechanics is expressed. The distant interactions of cause and effect are modeled by the propagation of waves from one local reference frame to another. The derivation of the equation of motion on a straight segment serves to express the proper acceleration as the sum of the accelerations imposed on it, in the form of an orthogonal local Helmholtz-Hodge decomposition, in one divergence-free and another curl-free contribution. I wrote the inertia term in the form of a gradient of a scalar potential and a dual curl of a vector potential. The adopted formalism opens the way to a reformulation of the material derivative in terms of potentials and allows me to remove the fictitious forces from continuum mechanics. The discrete equation of motion, invariant by rotation at constant angular velocity, is used to conserve the angular momentum per unit of mass, in addition to the conservation of energy per unit of mass and acceleration. All the variables in this equation are expressed only with two fundamental units, those of length and time.

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Inertial/kinetic-Alfvén wave turbulence: A twin problem in the limit of local interactions

Cited by 11 publications

References 55 publications

Wave turbulence in inertial electron magnetohydrodynamics

Wave turbulence in inertial electron magnetohydrodynamics

Locality of triad interaction and Kolmogorov constant in inertial wave turbulence

On Helmholtz–Hodge decomposition of inertia on a discrete local frame of reference

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