Helical flow can occur in porous media if the hydraulic conductivity tensor is anisotropic. We study the structure of steady-state flow fields in three-dimensional anisotropic porous media formed by two homogeneous layers, one of which is anisotropic. We simulate transient transport of a conservative scalar in such flow fields by a hybrid streamline/smoothed particle hydrodynamics method and analyze dilution. We use stretching and folding metrics to characterize the flow field and the dilution index of a conservative scalar divided by the volume of the domain to quantify plume dilution. Based on the results of detailed numerical simulations, we conclude that nonlinear deformation triggers dilution and that plume dilution is controlled by two parameters: the contrast between the principal directions of the anisotropic layer, and the orientation of the hydraulic conductivity tensor with respect to the main flow direction. Furthermore, we show that in this kind of flow fields transverse dispersion is responsible for an increase in plume dilution, while the effect of longitudinal dispersion is negligible.