CONICET | Buscador de Institutos y Recursos Humanos

Correlation anisotropy emerges dynamically in magnetohydrodynamics (MHD), producing stronger gradients across the large-scale mean magnetic ﬁeld than along it. This occurs both globally and locally, and has signiﬁcant implications in space and astrophysical plasmas, including particle scattering and transport, and theories of turbulence. Properties of local correlation anisotropy are further documented here by showing through numerical experiments that the effect is intensiﬁed in more localized estimates of the mean ﬁeld. The mathematical formulation of this property shows that local anisotropy mixes second-order with higher order correlations. Sensitivity of local statistical estimates to higher order correlations can be understood in connection with the stochastic coordinate system inherent in such formulations. We demonstrate this in speciﬁc cases, and illustrate the connection to higher order statistics by showing the sensitivity of local anisotropy to phase randomization, after which the global measure of anisotropy is recovered at all scales of averaging. This establishes that anisotropy of the local structure function is not a measure of anisotropy of the energy spectrum. Evidently, the local enhancement of correlation anisotropy is of substantial fundamental interest and must be understood in terms of higher order correlations, speciﬁcally fourth-order and above.