Tracer Transport through Seepage Lakes

Residence times of tracers in rectangular seepage lakes with wind-driven circulation are investigated in this paper. The key dimensionless parameters are $D_{T}W/q{L}_T^2$ and $VW/q{L}_L$, in which $D_T$ is the diffusion coefficient transverse to the wind direction, $W$ is the dimension of the lake aligned with the direction of groundwater inflow/outflow, $q$ is the specific discharge of groundwater entering and leaving the lake, $L_L$ and $L_T$ are the lake dimensions in the wind direction and transverse to the wind direction, respectively, and V is the wind speed. The well-mixed approximation in rectangular lakes is reasonable when $D_{T}W/q{L}_T^2>1$ and $VW/q{L}_L\gg 1$. Under these conditions, tracer particles are distributed uniformly over the outflow surface, and the probability distribution of tracer residence times can be estimated theoretically without the need to develop a numerical mixing model for the lake.