1999/09/14 by Itai Arad, I. Arad, Luca Biferale +3 · 4 citations
Biochemistry, Genetics and Molecular Biology · Engineering · Physics and Astronomy · #Characterization and Applications of Magnetic Nanoparticles #Geomagnetism and Paleomagnetism Studies #Solar and Space Plasma Dynamics #chao-dyn #nlin.CD
paper · pdf · doi:10.1103/physreve.61.2654
22 pages, 2 figures. Submitted to PRE
arxiv created 1999/09/14 · openalex publication_date 2000/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We address the scaling behavior of the covariance of the magnetic field in the three-dimensional kinematic dynamo problem when the boundary conditions and/or the external forcing are not isotropic. The velocity field is Gaussian, space homogeneous, and \ensuremathδ correlated in time, and its structure function scales with a positive exponent \ensuremathξ. The covariance of the magnetic field is naturally computed as a sum of contributions proportional to the irreducible representations of the SO(3) symmetry group. The amplitudes are nonuniversal, determined by boundary conditions. The scaling exponents are universal, forming a discrete, strictly increasing, spectrum indexed by the sectors of the symmetry group. When the initial mean magnetic field is zero, no dynamo effect is found, irrespective of the anisotropy of the forcing. The rate of isotropization with decreasing scales is fully understood from these results.