Occurence of Helical Flow in Cross-Bedded Sediments and Consequences for Transverse Mixing

Abstract:

Spatially variable orientation of anisotropy can cause helical flow in porous media. Previous studies predominantly analyzed systems in which stripes of materials with different hydraulic anisotropy are aligned with the mean direction of flow. Bakker and Hemker (2002, 2004) presented closed-form expressions for flow in uch systems, pointing to the occurrence of secondary flow. Chiogna et al. (2015) and Cirpka et al. (2015) analyzed locally isotropic hydraulic conductivity fields with blockwise constant anisotropic correlation structure showing that macroscopically helical flow evolves despite a local helicity density of zero. The latter studies also included various metrics to characterize the flow field and kinematic deformation (correlation structure of transverse velocity components, two-point semi-variogram of displacement, stretching, folding) and numerical simulations of steady-state advective-dispersive transport, analyzed by the flux-related dilution index emphasizing that helical flow causes an increase in transverse mixing that cannot be achieved by any other mechanism by which heterogeneity enhances transverse mixing. While these studies demonstrated the potential importance of helical flow in heterogeneous porous media the likelihood of its occurrence remained unclear. In particular, natural sediments do not exhibit extended stripes of materials with diagonally oriented internal anisotropy.
In the present study, we generated realistic looking sedimentary structures mimicking scour fills. The individual geobodies have a spoon-like shape and are filled with anisotropic porous material. Cross-sections show typical cross-bedding. In particular we analyzed how the variability in bulk hydraulic conductivity between the geobodies and the differences in the orientation of anisotropy affect flow and transverse solute mixing. While the variance of log-hydraulic conductivity controls longitudinal spreading and mixing, the variability in the orientation of anisotropy is decisive for folding and mixing perpendicular to the mean flow direction. The importance of non-stationary anisotropy for transverse mixing poses a challenge for the hydraulic characterization of sediments in the context of predicting lengths of quasi steady-state plumes.