We analyse the 3-D propagation of wind-forced near-inertial motions in a fully turbulent mesoscale eddy field with a primitive-equation numerical model. Although the wind-stress is uniform, the near-inertial motion field quickly becomes spatially heterogeneous, involving horizontal scales much smaller than the eddy scales. Analysis confirms that refraction by the eddy relative vorticity is the main mechanism responsible for the horizontal distortion of the near-inertial motions, which subsequently triggers their vertical propagation. An important result is the appearance of two maxima of near-inertial vertical velocity (both with r.m.s. values reaching 40 m/day): one at a depth of 100 m and another unexpected one much below the main thermocline around 1700 m. The shallow maximum, captured by the highest vertical normal modes, involves near-inertial motions with a spatial heterogeneity close to the eddy vorticity gradient field. These characteristics match analytical results obtained with Young and Ben Jelloul (1997)'s approach. The deep maximum, captured by the lowest vertical normal modes, involves superinertial motions with a frequency of twice the inertial frequency and much smaller horizontal scales. Because of these characteristics, not anticipated by previous analytical studies, these superinertial motions may represent an energy source for small-scale mixing through a mechanism not taken into account in the present study: the parametric subharmonic instability (PSI). This reveals a pathway by which wind energy may have a significant impact on small-scale mixing in the deep interior. Further studies that explicitly take into account PSI are needed to estimate this potential impact.