The direct numerical simulation of the flow over a sphere is performed. The computations are carried out in the sub-critical regime at Re = 3700 and Re = 10000 (based on the free-stream velocity and the sphere diameter). A parallel unstructured symmetry-preserving formulation is used for simulating the flow. Particular attention is devoted to investigate the shear-layer instabilities and its influence in the vortical structures in the wake of the sphere. Main features of the flow including power spectra of a set of selected monitoring probes at different positions are described and discussed in detail. Detailed information about turbulent statistics are also provided.