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The chaotic advection of fluid particle pairs is investigated though a low-order model of two-dimensional magnetohydrodynamic (MHD), where only five nonlinearly interacting modes are retained. The model is inthrinsically inhomogeneous and anisotropic because of the influence of large-scale fluctuations. Therefore, even though dynamically chaotic, the fields are unable to form the typical scaling laws of fully developed turbulence. Results show that a super-ballistic dynamics, reminiscent of the Richardson law of particle-pairs diffusion in turbulent flows, is robustly obtained using the truncated model. Indeed, even in the strongly reduced truncation presented here, particle diffusion in MHD turbulence has the same laws as the separation of velocity of particle pairs. The inherent anisotropy only affects the scaling of diffusivity, by enhancing the diffusion properties along one direction for small time-scales. Finally, when further anisotropy is introduced in the system through Alfvén waves, fluid particles are trapped by these, and super-ballistic diffusion is replaced by Brownian-like diffusion. On the other hand, when the magnetic field is removed, the kinetic counterpart of the model does not show super-ballistic dynamics.
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