  We generalize classical dispersion theory for a passive scalar to derive an
asymptotic long-time convection-diffusion equation for a solute suspended in a
wide, structured channel and subject to a steady low-Reynolds-number shear
flow. Our theory, valid for small roughness amplitudes of the channel, holds
for general surface shapes expandable as a Fourier series. We determine an
anisotropic dispersion tensor, which depends on the characteristic wavelengths
and amplitude of the surface structure. For surfaces whose corrugations are
tilted with respect to the applied flow direction, we find that dispersion
along the principal direction (i.e., the principal eigenvector of the
dispersion tensor) is at an angle to the main flow direction and becomes
enhanced relative to classical Taylor dispersion. In contrast, dispersion
perpendicular to it can decrease compared to the short-time diffusivity of the
particles. Furthermore, for an arbitrary surface shape represented in terms of
a Fourier decomposition, we find that each Fourier mode contributes at leading
order a linearly-independent correction to the classical Taylor dispersion
tensor.
