Averaging in non‐linear advective transport problems

Advective transport in a tidal basin is modelled by a non‐linear parabolic equation with initial‐boundary values. The model includes small effects such as diffusion, the reststream, reaction effects and sources. For a given periodic flow field, the long‐time behaviour of the solutions is approximated by using the averaging method. We show the existence of a periodic solution and we demonstrate the asymptotic validity of the approximations for all time using maximum principles.