Strong velocity gradients at granular borders appear to be the source of unresolved velocity fluctuations detectable as line broadening variations of magnetically and thermally insensitive absorption lines. Based on spectrograms of high spatial and spectral resolution taken with the German Vacuum Tower Telescope (VTT) in Izana (Tenerife) we study the strong velocity gradients and the unresolved velocity field as well as their mutual interaction. We also investigate the variation of these quantities with the height in the photosphere, for both a regular and an exploding granule. By means of a coherence analysis we study, furthermore, the extension of the convective and turbulent fluctuation field of the granulation layers into the overlying overshoot layers as a function of the wavenumber. The results of the coherence analysis are consistent with, and complementary to, those obtained from the investigation of regular and exploding granules. The small and large scales of the convective and unresolved velocity field behave clearly different as far as their penetration into the overlying photospheric layers is concerned. One pressure scale height above the continuum we find an unresolved velocity field that does not show any resemblance to the same velocity field at the continuum level. We find that the symmetry behavior of the unresolved velocity field with respect to the granular flow varies with the height in the photosphere. The unresolved velocity field could be of oscillatory, convective, or turbulent character. However, the fact that the unresolved velocity field is more prominent at the granular border, which is also the location of strong shear flow, favors its turbulent character. In this sense the granules can be seen as quasi-laminar convective flows emerging in the turbulent field of the overshoot layers.