Anisotropic fluxes and nonlocal interactions in MHD turbulence

Abstract

We investigate the locality or nonlocality of the energy transfer and of the spectral interactions involved in the cascade for decaying magnetohydrodynamic (MHD) flows in the presence of a uniform magnetic field $\mathbf{B}$ at various intensities. The results are based on a detailed analysis of three-dimensional numerical flows at moderate Reynold numbers. The energy transfer functions, as well as the global and partial fluxes, are examined by means of different geometrical wavenumber shells. On the one hand, the transfer functions of the two conserved Elsässer energies $E^{+}$ and $E^{-}$ are found local in both the directions parallel ($k_{\Vert }$-direction) and perpendicular ($k_{\perp }$-direction) to the magnetic guide-field, whatever the $\mathbf{B}$-strength. On the other hand, from the flux analysis, the interactions between the two counterpropagating Elsässer waves become nonlocal. Indeed, as the $\mathbf{B}$-intensity is increased, local interactions are strongly decreased and the interactions with small $k_{\Vert }$ modes dominate the cascade. Most of the energy flux in the $k_{\perp }$-direction is due to modes in the plane at $k_{\Vert }=0$, while the weaker cascade in the $k_{\Vert }$-direction is due to the modes with $k_{\Vert }=1$. The stronger magnetized flows tends thus to get closer to the weak turbulence limit where the three-wave resonant interactions are dominating. Hence, the transition from the strong to the weak turbulence regime occurs by reducing the number of effective modes in the energy cascade.

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References in corpus (14)

• A weak turbulence theory for incompressible MHD
• The Anisotropy of MHD Alfvénic Turbulence
• Simulations of Incompressible MHD Turbulence
• Statistical Theory of Magnetohydrodynamic Turbulence: Recent Results
• Shell to shell energy transfer in MHD, Part I: steady state turbulence
• Spectral energy dynamics in magnetohydrodynamic turbulence
• Shell to shell energy transfer in MHD, Part II: Kinematic dynamo
• Large scale flow effects, energy transfer, and self-similarity on turbulence
• The imprint of large-scale flows on turbulence
• On spectral scaling laws for incompressible anisotropic MHD turbulence
• Energy spectrum of turbulent fluctuations in boundary driven reduced magnetohydrodynamics
• Exact scaling laws and the local structure of isotropic magnetohydrodynamic turbulence
• Energy transfer and locality in magnetohydrodynamic turbulence
• Nonlocal Phenomenology for anisotropic MHD turbulence

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