Steady seepage flow to sink pairs symmetrically situated above and below a horizontal diffusing interface: 1. Parallel line sinks

Abstract

As an aid in understanding the flow regime close to a pair of wells situated on opposite sides of a diffusing interface between freshwater overlying saline water, an idealized symmetrical system is considered. The interface is assumed to be horizontal, and gravitational effects are neglected. A uniform flow is assumed to be parallel to the interface, and it is postulated that the fresh and saline fluids are separated by a thin impermeable layer at a finite distance upstream from the sinks. The edge of the impermeable layer provides a definite starting point for diffusive mixing at the interface. As part of a large‐scale gravity system, flow in the upper fluid should bear a qualitative resemblance to field situations where freshwater is moving slowly over saltwater almost at rest. Boundary layer theory is used to treat the growth of the diffusive mixing layer, modified by the presence of the sinks, and the flux of salt to the upper sink is calculated as a function of the spacing and strength of the uniform flow. A periodic system of sink pairs without an applied flow is also considered. Exact solutions of the boundary layer equations are readily obtained for the two‐dimensional case. An approximate treatment of the system comprising a pair of point sinks in a uniform flow is deferred until part 2.