Integral transforms for three-dimensional steady turbulent dispersion in rivers and channels

A three-dimensional steady-state mathematical model is considered for predicting the fate of dissolved contaminants in rivers and channels under turbulent flow conditions. The model allows for variable velocity fields and non-uniform turbulent diffusivities within channels of rectangular cross sections. Making use of the Generalized Integral Transform Technique (GITT), a hybrid numerical–analytical solution for the concentration fields is then obtained. The solution convergence behavior is investigated and the criterion for reordering the terms in the infinite series is discussed, with the aim of reducing the computational effort associated with the multiple eigenfunction expansions. A test case is presented to illustrate the proposed approach.