An analytic assessment of the role of anisotropic corrections to the isotropic anomalous scaling exponents is given for the d-dimensional kinematic magnetohydrodynamics problem in the presence of a mean magnetic field. The velocity advecting the magnetic field changes very rapidly in time and scales with a positive exponent \xi. Inertial-range anisotropic contributions to the scaling exponents, \xi_j , of second-order magnetic correlations are associated with zero modes and have been calculated nonperturbatively. For d=3, the limit \xi \to 0 yields ?j?j?2??(2j3?j2?5j?4)/?2(4j2?1)?, where j (j?2) is the order in the Legendre polyno- mial decomposition applied to correlation functions. Conjectures on the fact that anisotropic components cannot change the isotropic threshold to the dynamo effect are also made.
Anisotropic non-perturbative zero modes for passively advected magnetic fields
A S Lanotte;
1999
Abstract
An analytic assessment of the role of anisotropic corrections to the isotropic anomalous scaling exponents is given for the d-dimensional kinematic magnetohydrodynamics problem in the presence of a mean magnetic field. The velocity advecting the magnetic field changes very rapidly in time and scales with a positive exponent \xi. Inertial-range anisotropic contributions to the scaling exponents, \xi_j , of second-order magnetic correlations are associated with zero modes and have been calculated nonperturbatively. For d=3, the limit \xi \to 0 yields ?j?j?2??(2j3?j2?5j?4)/?2(4j2?1)?, where j (j?2) is the order in the Legendre polyno- mial decomposition applied to correlation functions. Conjectures on the fact that anisotropic components cannot change the isotropic threshold to the dynamo effect are also made.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
