Persistence of small-scale anisotropies and anomalous scaling in a model of magnetohydrodynamics turbulence

The problem of anomalous scaling in magnetohydrodynamics turbulence is cons idered within the framework of the kinematic approximation, in the presence of a large-scale background magnetic field. The velocity field is Gaussian , delta-correlated in time, and scales with a positive exponent xi. Explici t inertial-range expressions for the magnetic correlation functions are obt ained; they are represented by superpositions of power laws with nonunivers al amplitudes and universal (independent of the anisotropy and forcing) ano malous exponents. The complete set of anomalous exponents for the pair corr elation function is found nonperturbatively, in any space dimension d, usin g the zero-mode technique. For higher-order correlation functions, the anom alous exponents are calculated to O(xi) using the renormalization group. Th e exponents Exhibit a hierarchy related to the degree of anisotropy; the le nding contributions to the even correlation functions are given by the expo nents from the isotropic shell, in agreement with the idea of restored smal l-scale isotropy. Conversely, the small-scale anisotropy reveals itself in the odd correlation functions: the skewness factor is slowly decreasing goi ng down to small scales and higher odd dimensionless ratios (hyperskewness, etc.) dramatically increase. thus diverging in the r-->0 limit.