Large-Eddy Simulation is adopted to reproduce the wake of an axial-flow hydrokinetic turbine. The process of momentum recovery is correlated with the destabilization of the wake system, starting wake contraction and radial flows from the free-stream towards the wake core. All terms of the momentum balance equation are analyzed. The radial advection dominates the momentum recovery at the outer radii (in the vicinity of the radial boundary of the wake), just downstream of the instability of the system of tip vortices. Further downstream the reduction of the mean radial gradients makes advection less significant and the radial turbulent transport becomes the main source of momentum replenishment at inner radii, near the wake axis. The details of the process of momentum recovery and its correlation with the instability of the wake system, revealed by the present high-fidelity eddy-resolving computations, provide new insight on the development of the wake of axial-flow hydrokinetic turbines.