Anisotropies have been observed in the TeV-PeV cosmic ray (CR) flux at Earth, both at large and small angular scales. While the CR diffusion approximation predicts a dipole amplitude comparable to that observed (approximate to 10(-3)), it cannot explain anisotropies at smaller scales. In this work, we demonstrate that energy dependent smaller scale anisotropies necessarily appear on the sky, provided a large scale anisotropy exists {[}1]. They are due to the local turbulent magnetic field configuration within the CR scattering length.