Dear Abhinav,
I don’t really know how you’ve set up your simulation, so, it is difficult for me to comment on the results, but it appears that it is the tower natural frequency that has been excited (about 3-s period, or 1/3 Hz) and is damping out very slowly. I don’t really see much effect of the turbulence.
Regarding the comparison to HAWC2, one problem with FAST v7 was the inability to model direct wind (drag) loads on the tower, which likely dominate the tower loads when running simulations in high winds with the rotor parked or idling with the blades fully feathered and the shaft aligned with the mean wind direction. FAST v8 enables you to model the tower wind loads; it may be appropriate to upgrade. The NREL 5-MW turbine atop the OC3-monopile (in 20-m water depth) is available as Test19 in the FAST v8 archive.
Best regards,