  We develop a theory of enhanced diffusivity and skewness of the longitudinal
distribution of a diffusing tracer advected by a periodic time-varying shear
flow in a straight channel. Although applicable to general fluid flow, we
restrict the examples of our theory to the tracer advected by flows that are
induced by a periodically oscillating wall in a Newtonian fluid between two
infinite parallel plates as well as flow in an infinitely long duct. We first
derived the formula of the flow produced by the wall motions. Second, we
calculate the second Aris moment for all time and its long-time limiting
effective diffusivity as a function of the geometrical parameters, frequency,
viscosity, and diffusivity. Using a new formalism based upon the Helmholtz
operator we establish a new single series formula for the variance. We show
that the viscous-dominated limit results in a linear shear layer for which the
effective diffusivity is bounded. For finite viscosities, the enhanced
diffusion diverges in the high-frequency limit. We present a study of the
effective diffusivity surface as a function of the non-dimensional parameters
which shows how a maximum can exist for various parameter sweeps. Physical
experiments are performed in water using particle tracking velocimetry to
quantitatively measure the fluid flow. Using fluorescein dye as the passive
tracer, we document that the theory is quantitatively accurate. Specifically,
image analysis suggests that the distribution variance be measured using the
full width at half maximum is robust to noise. Further, we show that the scalar
skewness is zero for linear shear flows at all times, whereas for the nonlinear
Stokes layer, the skewness sign can be controlled through the oscillating
phase. Last, for single-frequency wall motion, the long-time skewness decays at
the faster rate as compared with the case with steady flow.
