Impact of the spatial structure of the hydraulic conductivity field on vorticity in three-dimensional flows

Abstract

A material fluid element within a porous medium experiences deformations due to the disordered spatial distribution of the Darcy scale velocity field, caused by the heterogeneity of hydraulic conductivity. A physical consequence of this heterogeneity is the presence of localized kinematical features such as straining, shearing and vorticity in the fluid element. These kinematical features will influence the shape of solute clouds and their fate. Studies on the deformation of material surfaces highlighted the importance of stretching and shearing, whereas vorticity received so far less attention, though it determines folding, a deformation associated with the local rotation of the velocity field. We study vorticity in a three-dimensional porous formation exploring how its fluctuations are influenced by the spatial structure of the porous media, obtained by immersing spheroidal inclusions into a matrix of constant hydraulic conductivity. By comparing porous formations with the same spatial statistics, we analyse how vorticity is affected by the different shape and arrangement of inclusions, defined as the medium 'microstructure'. We conclude that, as microstructure has a significant impact on vorticity fluctuations, the usual second-order statistical description of the conductivity field is unable to capture local deformations of the plume

Under What Conditions Does Transverse Macrodispersion Exist in Groundwater Flow?

“…(2003, 2009) and Di Dato, Fiori, et al. (2016); Di Dato, de Barros et al. (2016) find transverse macrodispersion occurs in steady 3D Darcy flow with non‐smooth isotropic hydraulic conductivity fields.…”

Effects of the hydraulic conductivity microstructure on macrodispersivity

“…This deformation is also influenced by the microstructure, i.e., orientation and elongation of inclusions, and consequently α T is larger for smaller and for prolate than oblate inclusions. Transverse streamline deformation is in fact much less pronounced for low‐conductive inclusions, due to the lack of focusing‐defocusing effects (streamlines tend to bypass to low‐conductivity inclusion, rather than being attracted as it occurs for highly conductive inclusions) [ Di Dato et al ., ]. As an effect of the different dependence of macrodispersion from κ and , the ratio is larger for high‐conductive inclusions than for low‐conductivity inclusions, with important consequences in applications, since transverse dispersion is often assumed as a fraction of longitudinal dispersion, with occurring the most, despite the importance of transverse dispersion as controlling factor of natural attenuation in steady state plumes [ Liedl et al ., ; Cirpka et al ., ; Zarlenga and Fiori , ].…”

“…where r is the lag distance vector along the direction with respect to which the integral scale is evaluated and r jrj is its module. The detailed procedure used to compute the integral scale is provided in Di Dato et al [2016].…”