  Direct numerical simulations (DNSs) of turbulent pipe flow subjected to
streamwise-varying wall rotation are performed. This control method is able to
achieve drag reduction and even relaminarize the flow under certain control
parameters at low Reynolds number. Two control parameters, which are velocity
amplitude and wavelength, are considered. An annular boundary layer, called
Spatial Stokes Layer (SSL), is formed by the wall rotation. Based on the
thickness of SSL, two types of drag reduction scenarios are identified. When
the thickness is low, the SSL acts as a spacer layer, obstructing the impact of
fluids against the wall and hence reducing the shear stress. The flow
structures in the outer layer are less affected and are stretched in streamwise
direction due to the increased velocity gradient. Within the SSL, the
turbulence intensity diminishes dramatically. When the thickness is large, a
streamwise wavy pattern of near-wall low-speed streaks is formed. The
orientation of streaks is found to lag behind the direction of local mean
velocity in phase and conform to the direction of local resultant shear stress.
The streamwise scale of near-wall flow structures is significantly reduced,
resulting in the disruption of downstream development of flow structures and
hence leading to the drag reduction. Besides, it is found that it requires both
large enough thickness of SSL and velocity amplitude to relaminarize the
turbulence. The relaminarization mechanism is that the annular SSL can
continuously absorb energy from wall-normal stress due to the rotation effect,
thereby the turbulence self-sustaining process could not be maintained. For the
relaminarization cases, the laminar state is stable to even extremely large
perturbations, which possibly makes laminar state the only fixed point for the
whole system.
