Modeling the Influence of a Variable Permeability Inclusion on Free‐Surface Flow in an Inclined Aquifer

The interaction of sub-surface, gravity-driven flows with inclusions different permeabilities are investigated theoretically using a model that exploits the relative shallowness motion. Numerically computed solutions for steady motion around cylindrical reveal range behaviors dependent on ratio interior to exterior permeability and dimensionless flow parameter measures far-field thickness product gradient slope down which fluid width inclusion. When inclusion is relatively narrow, depth little changed from its value focused into higher deflected those lower permeability. However, if wide then three qualitatively regimes emerge, permeabilities. similar, negligible deviation occurs apart within thin transition layers at boundary differ significantly, forms deep ponds either upstream or downstream low high inclusion, respectively, arise due deflection focusing. In each case, asymptotic relationships derived between parameters. Inclusions differing cross-section also analyzed numerically analytically draw out interplay adjustment,