Manifestation of anisotropy persistence in the hierarchies of magnetohydrodynamical scaling exponents

An example of a turbulent system where the failure of the hypothesis of sma ll-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. Spec ifically, within the kinematic approximation in magnetohydrodynamical turbu lence, we show that for compressible flows, the isotropic contribution to t he scaling of magnetic correlation functions and the first anisotropic ones may become practically indistinguishable. Moreover, the skewness factor no w diverges as the Peclet number goes to infinity, a further indication of s mall-scale anisotropy.