The dipole anisotropy of multi-TeV cosmic rays exhibits a strong energy dependence that is at odds with the predictions of standard isotropic diffusion models. It has been argued that the observed variation in amplitude and phase is a consequence of the global distribution of cosmic ray sources in combination with anisotropic diffusion in our local environment. For a quantitative description of this effect it is necessary to understand the complicated interplay of cosmic ray diffusion on local and global scales. In this work we study the impact of isotropic magnetic turbulence realisations on cosmic-ray propagation and anisotropy. We define a novel methodology that allows us to quantify generic properties of local and global diffusion with the help of test-particle simulations. We confirm the emergence of local anisotropic diffusion that leads to an alignment of the cosmic ray dipole with the local magnetic field and a reduction of its amplitude in perpendicular directions. We discuss the phenomenological consequences of these findings.