Modelling the influence of a variable permeability inclusion on free‐surface flow in an inclined aquifer

Abstract

The interaction of sub-surface, gravity-driven flows with inclusions of different permeabilities are investigated theoretically using a model that exploits the relative shallowness of the motion. Numerically computed solutions for steady motion around cylindrical inclusions reveal a range of behaviors dependent on the ratio of the interior to exterior permeability and a dimensionless flow parameter that measures the far-field thickness to the product of the gradient of the slope down which the fluid flows and the width of the inclusion. When the inclusion is relatively narrow, the depth of the flow is little changed from its far-field value and the fluid is focused into inclusions of higher ..