Distribution of the velocity modulus for the numerical tests described in Sect. 2.1. From top left to bottom right: a) background velocity profile with α =  −1 and N = 10 additional patches of turbulent field with σ_v/v_o = 0.3; b) same as a), but with α =  −0.5; c) same as a), but with α =  −0.1; d) same as b), but with N = 50; e) only background velocity field with α =  −0.5, no turbulent patches; f) as in b), but with turbulent patches everywhere; g) as in b), but assuming an outer scale of turbulent motions k_in = 5; h) as in b), but assuming an outer scale of turbulent motions k_in = 1. In each panel, the black lines show the total input velocity field, the blue lines the input turbulent field, and the red lines the field reconstructed with our algorithm.