  The propagation of cosmic rays (CRs) in turbulent interstellar magnetic
fields is typically described as a spatial diffusion process. This formalism
predicts only a small deviation from an isotropic CR distribution in the form
of a dipole in the direction of the CR density gradient or relative background
flow. We show that the existence of a global CR dipole moment necessarily
generates a spectrum of higher multipole moments in the local CR distribution.
These "anomalous" anisotropies are a direct consequence of Liouville's theorem
in the presence of a local turbulent magnetic field. We show that the
predictions of this model are in excellent agreement with the observed power
spectrum of multi-TeV CRs.
