  Direct numerical simulations of turbulent pipe flow subjected to
streamwise-varying wall rotation are performed. This control method is observed
to be able to significantly reduce the friction drag and even laminarize the
flow under certain control parameters, which are dictated by velocity amplitude
and wavelength, for friction Reynolds number Re{\tau} =180. Net energy saving
is achievable and the variation of wavelength is found to be more efficient
than velocity amplitude in reducing the drag. A series of turbulence statistics
are discussed in order to elucidate the impact of steady spatially oscillatory
forcing, including budgets of transport equation, turbulence intensity,
two-point correlation and one-dimensional spectra. An overall assessment of
global energy balance identifies a trend toward laminar regime. The
control-induced boundary layer, whose thickness is closely related to control
wavelength, is shown to induce a streamwise wavy streak pattern, with its
orientation governed by the shear force stemming from gradients of mean
velocity. Such strong spatial non-homogeneity is found to significantly reduce
the streamwise scale of flow structure. The analysis of conditional-averaged
fields reveals an emergence of strong transverse advection, which is observed
to cause asymmetrical modification of near-wall quasi-streamwise vortex pair,
accompanied by the transverse tilt or diffusion of low-speed streaks and the
suppression of its surrounding sweep events, leading to the disruption of
near-wall quasi-organized flow structure and hence in turn contributing to the
decline of turbulent shear stress.
