Transition from weak to strong cascade in MHD turbulence

Abstract

The transition from weak to strong turbulence when passing from large to small scales in magnetohydrodynamic (MHD) turbulence with guide field is a cornerstone of anisotropic turbulence theory. We present the first check of this transition, using the Shell-RMHD which combines a shell model of perpendicular nonlinear coupling and linear propagation along the guide field. This model allows us to reach Reynolds numbers around $10^6$. We obtain surprisingly good agreement with the theoretical predictions, with a reduced perpendicular energy spectrum scaling as $k^{-2}$ at large scales and as $k^{-5/3}$ at small scales, where critical balance between nonlinear and propagation time is reached. However, even in the strong regime, a high level of excitation is found in the weak coupling region of Fourier space, which is due to the rich frequency spectrum of large eddies. A corollary is that the reduced parallel spectral slope is not a definite test of the spectral anisotropy, contrary to standard belief.

4 pages, 5 figures, accepted in PRL

References in corpus (5)

• Anisotropic scaling of magnetohydrodynamic turbulence
• Coronal Heating, Weak MHD Turbulence and Scaling Laws
• A Weakened Cascade Model for Turbulence in Astrophysical Plasmas
• Coronal heating in coupled photosphere-chromosphere-coronal systems: turbulence and leakage
• Weak Alfven-Wave Turbulence Revisited

Cited by in corpus (13)

• Shell Models of Magnetohydrodynamic Turbulence
• Direct Evidence of the Transition from Weak to Strong MHD Turbulence
• Critical Balance and the Physics of MHD Turbulence
• Turbulent Reconnection in Relativistic Plasmas And Effects of Compressibility
• Resonance Broadening and Heating of Charged Particles in Magnetohydrodynamic Turbulence
• Beyond the Maltese cross: geometry of turbulence between 0.2 and 1 AU
• Weak Alfvénic turbulence in relativistic plasmas II: Current sheets and dissipation
• Identification of the weak-to-strong transition in Alfvénic turbulence from space plasma
• Three-dimensional local anisotropy of velocity fluctuations in the solar wind
• Intermittency in Hall-magnetohydrodynamics with a strong guide field
• Reynolds number dependence of Lagrangian dispersion in direct numerical simulations of anisotropic magnetohydrodynamic turbulence
• Shell Models on Recurrent Sequences: Fibonacci, Padovan and Other Series
• Nonlinear phase synchronization and the role of spacing in shell models