Tidally averaged models for dispersion in shallow water

Abstract

This paper deals with the advection and diffusion of contaminants in tidal waters. The analysis starts with the well‐known vertically integrated advection‐diffusion equation. In order to derive a tidally averaged model to describe the advection and dispersion processes over long periods and to gain insight into the tidally induced dispersion, a new method to average the tide is introduced. Here it is assumed that both the dispersion coefficient and the residual flow are sufficiently small. The averaging procedure is derived by using a random walk model to describe the dispersion process. This random walk model is shown to be exactly consistent with the advection‐diffusion equation. The averaging procedure results in equations for the averaged advective transport as well as equations for the effective dispersion tensor describing the mixing process that occurs within one tidal cycle. By using a numerical model to determine the tidal movement over one tidal cycle, the tidally averaged advective transport and dispersion tensor in each grid point of the model is approximated numerically. In this way a tidally induced dispersion map of the area under study is obtained.