Dynamical Effects of Variations of Conduit Area in a Karst Conduit

Variations of the cross-sectional area of a conduit embedded within a porous medium have two effects on flow and transport. First, the hydraulic gradient required to convey a specified flux of water is increased. Second, local exchanges of water and pollutants between the conduit and surrounding porous medium are induced, forming a hyporheic zone. Both these effects are quantified in the case that the variations are periodic and the fractional change of conduit flux induced by the variations is small. The resistance to flow increases dramatically as the variations increase in amplitude. The volume of the hyporheic zone is proportional to the square of the wavelength of the variations. If the wavelength is large, the volume of the hyporheic zone can be far larger than that of the conduit, permitting the sequestration of contaminants for long periods of time.