Nonlocal Phenomenology for Anisotropic Magnetohydrodynamic Turbulence

A nonlocal cascade model for anisotropic magnetohydrodynamic (MHD) turbulence in the presence of a uniform magnetic field B is proposed. The model takes into account that (1) 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 B field is made, and (2) the interactions that result in the cascade are between different scales. Eddies with wavenumbers and interact with eddies with wavenumbers qk, q⊥ such that a resonance condition between the wavenumbers k k k ⊥ qk, q⊥ and kk, k⊥ holds. As a consequence, energy from the eddy with wavenumbers and cascades due to k k k ⊥ interactions with eddies located in the resonant manifold whose wavenumbers are determined by q k and , and energy will cascade along the lines . For a uniform energy injection 1/3 2/3 2/3 1/3 e k /B q k k k k e /B ⊥ ⊥ ⊥ k 0 ⊥ rate in the parallel direction, the resulting energy spectrum is . For a general forcing, however, 2/3 1 5/3 E(k ,k ) e k k k ⊥ k ⊥ the model suggests a nonuniversal behavior. The connections with previous models, numerical simulations and weak turbulence theory are discussed. Subject headings: magnetic fields — MHD — solar wind — turbulence