Manifestation of anisotropy persistence in the hierarchies of magnetohydrodynamical scaling exponents

An example of a turbulent system where the failure of the hypothesis of small-scale isotropy restoration is detectable both in the "flattening" of the inertial-range scaling exponent hierarchy and in the behavior of odd-order dimensionless ratios, e.g., skewness and hyperskewness, is presented. Specifically, within the kinematic approximation in magnetohydrodynamical turbulence, we show that for compressible flows, the isotropic contribution to the scaling of magnetic correlation functions and the first anisotropic ones may become practically indistinguishable. Moreover, the skewness factor now diverges as the Peclet number goes to infinity, a further indication of small-scale anisotropy.