TRACER ADVECTION BY STEADY GROUNDWATER-FLOW IN A STRATIFIED AQUIFER

The perfectly stratified aquifer has often been investigated as a simp le, tractable model for exploring new theoretical issues in subsurface hydrology. Adopting this approach, we show that steady groundwater fl ows in the perfectly stratified aquifer are always confined to a set o f nonintersecting permanent surfaces, on which both streamlines and vo rticity lines lie. This foliation of the flow domain exists as well fo r steady groundwater flows in any isotropic, spatially heterogeneous a quifer. In the present model example it is a direct consequence of the existence of a stream function, we then demonstrate that tracer plume advection by steady groundwater flow in a perfectly stratified aquife r is never ergodic, regardless of the initial size of the tracer plume . This nonergodicity, which holds also for tracer advection in any iso tropic, spatially heterogenous aquifer, implies that stochastic theori es of purely advective tracer plume movement err in assuming ergodic b ehavior to simplify probabilistic calculations of plume spatial concen tration moments.