Accepted for publication in MNRAS, 13 pages, 10 figuresInternational audienceThis paper combines observational datasets and cosmological simulations to generate realistic numerical replicas of the nearby Universe. These latter are excellent laboratories for studies of the non-linear process of structure formation in our neighborhood. With measurements of radial peculiar velocities in the Local Universe (cosmicflows-2) and a newly developed technique, we produce Constrained Local UniversE Simulations (CLUES). To assess the quality of these constrained simulations, we compare them with random simulations as well as with local observations. The cosmic variance, defined as the mean one-sigma scatter of cell-to-cell comparison between two fields...