Limitations of an analytical solution for advection - Diffusion with spatially variable coefficients

The aim of the article is to show that a published analytical solution for advection-diffusion in streams is of limited relevance. The analytical solution is based on the assumptions that the velocity increases linearly with distance and that the diffusion coefficient increases quadratically with distance. This implies that a solute concentration profile travelling down the channel is submitted to a stretching effect, due to continuity, that completely counteracts the effect of the increase in the diffusion coefficient. Therefore, these particular assumptions are equivalent to the simpler case of uniform velocity and diffusion coefficient, as far as the effect of diffusion is concerned. Two examples are proposed where results of a solute transport simulation using a semi-Lagrangian numerical model were compared to results using this analytical solution. Copyright © 2005 John Wiley & Sons, Ltd.