We detect and measure velocity fields because their Doppler shifts do the shaping and broadening of most spectral lines. The Doppler shifts of rotation dominate in most hot stars, but in cool stars, those to the cool side of the granulation and rotation boundaries, macroturbulence velocities are about the same size as those of rotation. Fourier analysis has proved to be very useful for measuring rotation rates and in separating rotational from macroturbulence broadening. Macroturbulence is almost certainly mainly granulation, but will contain all other Doppler broadening as well, such as non-radial oscillations.
The characteristic size of macroturbulence has been mapped across the cool half of the H-R diagram, and it is found to decline toward cooler and fainter stars.
Although a Gaussian distribution of velocities seems to work in the modeling, these velocities are not isotropic; neither is granulation, so we shouldn't be surprised. When a non-isotropic velocity distribution is integrated across the apparent disk of the star (as must be done in the modeling to compare with observations), the result is very definitely not a Gaussian. Furthermore, it is incorrect to use a convolution of this integrated Doppler-shift distribution with the other distributions of Doppler shifts, especially rotation. Instead, disk integrations must be computed. In some cases, the convolution approximation may be acceptable for handling the thermal profile.
These results and some of the details can be seen in the references: