Large-Eddy Simulation on a grid composed of about two billion points is utilized to characterize the turbulent wake of an axial-flow hydrokinetic turbine. The dominant role of the tip vortices is revealed, both in the near wake, where they are very coherent, and downstream, after development of instability. As long as the tip vortices are stable, sharp peaks of Reynolds stresses populate the outer boundary of the wake, where turbulence is strongly anisotropic and dominated by the fluctuations of the radial velocity component. Such anisotropy is also confirmed by the shear stresses, with the most significant one tied to the fluctuations of the radial and streamwise velocities, originating from the interaction between tip vortices. When the system of tip vortices develops instability, the behavior of turbulence is substantially modified. The outer maxima become more diffused and move gradually towards the wake core. In contrast with the near wake, the fluctuations of the radial velocity become lower than those of the azimuthal and streamwise velocities. Instead, the shear stress associated to the radial and streamwise velocities keeps the most significant one, contributing to momentum recovery via turbulent transport. The present results demonstrate a strong anisotropy of turbulence within the wake, which should be taken properly into account when lower-fidelity methodologies, relying on turbulence modeling, are utilized to simulate this class of flows.