  We use multiwavelength imaging observations from the Atmospheric Imaging
Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) to study the
evolution of Kelvin-Helmholtz (K-H) instability in a fan-spine magnetic field
configuration. This magnetic topology exists near an active region AR12297 and
is rooted in a nearby sunspot. In this magnetic configuration, two layers of
cool plasma flow in parallel and interact with each other inside an elongated
spine. The slower plasma flow (5 $km s^{-1}$) is the reflected stream along the
spine field lines from the top, which interacts with the impulsive plasma
upflows (114-144 km s$^{-1}$) from below. This process generates a shear motion
and subsequent evolution of the K--H instability. The amplitude and
characteristic wavelength of the K-H unstable vortices increase, satisfying the
criterion of the fastest growing mode of this instability. We also describe
that the velocity difference between two layers and velocity of K-H unstable
vortices are greater than the Alfven speed in the second denser layer, which
also satisfies the criterion of the growth of K-H instability. In the presence
of the magnetic field and sheared counter streaming plasma as observed in the
fan-spine topology, we estimate the parametric constant, $\Lambda\ge$1, that
confirms the dominance of velocity shear and the evolution of the linear phase
of the K-H instability. This observation indicates that in the presence of
complex magnetic field structuring and flows, the fan-spine configuration may
evolve into rapid heating, while the connectivity changes due to the
fragmentation via the K-H instability.
