A parametric study of laminar torsional Couette flow between a rotating flat disk and a stationary wavy disk is conducted using computer simulations. The waviness of the stationary disk, characterized by the parameter wave slope (WS), is increased across four cases to evaluate its influence. The resulting flow field is significantly different from torsional Couette flow between flat disks. Shear stress and pressure on the flat and wavy disks are sinusoidal with the same spatial frequency as the undulation. Their averages over one wavelength remain unaffected by the increase in WS. However, this is not the case with their amplitudes. A critical layer is observed approximately at a distance of 70% radius of the disk across which the effect of WS on shear amplitude is inverted. Furthermore, the sinusoidal shear on the flat disk is observed to be in destructive phase with respect to the shear on wavy disk. This is corroborated by the concave/convex distortion of the height-wise tangential velocity profile across the undulation. Alternately, the net radial velocity becomes biased either toward or away from the axis depending on angular location with respect to the undulation. The effect of increasing WS on the tangential velocity is in the form of small increments to the curvature of its height-wise profile, while the axial velocity, though it is orders of magnitude smaller than the tangential velocity, increases substantially with increase in WS.