  Relativistic AGN jets exhibit multi-timescale variability and a broadband
non-thermal spectrum extending from radio to gamma-rays. These highly
magnetized jets are prone to undergo several Magneto-hydrodynamic (MHD)
instabilities during their propagation in space and could trigger jet radiation
and particle acceleration. This work aims to study the implications of
relativistic kink mode instability on the observed long-term variability in the
context of the twisting in-homogeneous jet model. To achieve this, we
investigate the physical configurations preferable for forming kink mode
instability by performing high-resolution 3D relativistic MHD simulations of a
portion of highly magnetized jets. In particular, we perform simulations of
cylindrical plasma column with Lorentz factor $\geq 5$ and study the effects of
magnetization values and axial wave-numbers with decreasing pitch on the onset
and growth of kink instability. We have confirmed the impact of axial
wave-number on the dynamics of the plasma column including the growth of the
instability. In this work, we have further investigated the connection between
the dynamics of the plasma column with its time-varying emission features. From
our analysis, we find a correlated trend between the growth rate of kink mode
instability and the flux variability obtained from the simulated light curve.
