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 106. 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.
Transition from Weak to Strong Cascade in MHD Turbulence / A. Verdini;R. Grappin. - In: PHYSICAL REVIEW LETTERS. - ISSN 0031-9007. - STAMPA. - 109:(2012), pp. 025004-025009. [10.1103/PhysRevLett.109.025004]
Transition from Weak to Strong Cascade in MHD Turbulence
VERDINI, ANDREA;
2012
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 106. 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.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.