Direct and large-eddy simulations of the turbulent flow in a concentric annulus with or without inner wall rotation were performed at $Re_{D_h}$ = 8900. The main emphasis of this work was placed on the alteration of the near-wall turbulent structures due to transverse curvature and rotation of the inner wall. The turbulent structures close to the wall were scrutinized by computing the lower-order statistics. A quadrant analysis of the Reynolds shear stress was explored to develop a sufficiently complete picture of the contribution of flow events to turbulence production(consumption). The probability density functions of the velocity fluctuations and the splat/anti-splat process were examined to show the contributions of the flow events to turbulent production. The present numerical results indicated that the alteration of the near-wall turbulent structures could be attributed to the different vortex regeneration processes between the inner and outer walls and the destabilizing effect of rotation of the inner wall.