  We report on a three-dimensional MHD numerical experiment of a small scale
coronal mass ejection (CME) -like eruption propagating though a non-magnetized
solar atmosphere. We find that the Kelvin-Helmholtz instability (KHI) develops
at various but specific locations at the boundary layer between the erupting
field and the background atmosphere, depending on the relative angle between
the velocity and magnetic field. KHI develops at the front and at two of the
four sides of the eruption. KHI is suppressed at the other two sides of the
eruption. We also find the development of Alfv\'enic vortex shedding flows at
the wake of the developing CME due to the 3D geometry of the field. Forward
modeling reveals that the observational detectability of the KHI in solar
eruptions is confined to a narrow $\approx10^{\circ}$ range when observing
off-limb, and therefore its occurrence could be underestimated due to
projection effects. The new findings can have significant implications for
observations, for heating and for particle acceleration by turbulence from
flow-driven instabilities associated with solar eruptions of all scales.
