Nonlocal Phenomenology for anisotropic MHD turbulence

Abstract

A non-local cascade model for anisotropic MHD turbulence in the presence of a guiding magnetic field is proposed. The model takes into account that (a) energy cascades in an anisotropic manner and as a result a different estimate for the cascade rate in the direction parallel and perpendicular to the guiding field is made. (b) the interactions that result in the cascade are between different scales. Eddies with wave numbers $k_{\Vert }$ and $k_{\perp }$ interact with eddies with wave numbers $q_{\Vert },q_{\perp }$ such that a resonance condition between the wave numbers $q_{\Vert },q_{\perp }$ and $k_{\Vert },k_{\perp }$ holds. As a consequence energy from the eddy with wave numbers $k_{\Vert }$ and $k_{\perp }$ cascades due to interactions with eddies located in the resonant manifold whose wavenumbers are determined by: $q_{\Vert }\simeq {\epsilon }^{1/3}{k}_{\perp }^{2/3}/B$, $q_{\perp }=k_{\perp }$ and energy will cascade along the lines $k_{\Vert }\sim C+k_{\perp }^{2/3}{\epsilon }^{1/3}/B_0$. For a uniform energy injection rate in the parallel direction the resulting energy spectrum is $E(k_{\Vert },k_{\perp })\simeq {\epsilon }^{2/3}{k}_{\Vert }^{-1}{k}_{\perp }^{-5/3}$. For a general forcing however the model suggests a non-universal behavior. The connections with previous models, numerical simulations and weak turbulence theory are discussed.

arXiv commentSubmited to Astophys. Lett

References in corpus (11)

• A weak turbulence theory for incompressible MHD
• The Anisotropy of MHD Alfvénic Turbulence
• Simulations of Incompressible MHD Turbulence
• On the Spectrum of Magnetohydrodynamic Turbulence
• Shell to shell energy transfer in MHD, Part I: steady state turbulence
• Spectral energy dynamics in magnetohydrodynamic turbulence
• On spectral scaling laws for incompressible anisotropic MHD turbulence
• Energy spectrum of turbulent fluctuations in boundary driven reduced magnetohydrodynamics
• On the Nature of Incompressible Magnetohydrodynamic Turbulence
• Exact scaling laws and the local structure of isotropic magnetohydrodynamic turbulence
• Energy transfer and locality in magnetohydrodynamic turbulence

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