Scale-dependent dispersion from a pit

It is fairly well accepted that contaminant transport in aquifers can be modelled accurately only if dispersion coefficients are allowed to increase with distance downstream. However, this also increases the difficulty of obtaining exact solutions of the contaminant transport equation. Therefore, singular perturbation methods are used to obtain a relatively simple approximate solution for scale-dependent dispersion from a pit located in a region of uniform flow. Comparison of exact and approximate perturbation solutions for two simpler but related problems suggests that the perturbation approach used here is likely to give sufficient accuracy for many, if not most, applications.