Transverse mixing in natural channels

Abstract

A mathematical model is presented for predicting the steady state two‐dimensional distribution of solute concentration in a meandering nonuniform natural channel. Two features of the convection‐diffusion (mixing) equation derived herein are that it employs the transverse cumulative discharge as an independent variable replacing the transverse distance and that it is developed in an orthogonal curvilinear (natural) coordinate system which follows the general direction of the channel flow. With the help of the continuity equation of water the transverse convection term which cannot be neglected in a natural channel is eliminated from the mixing equation by a transformation wherein cumulative discharge replaces transverse distance. Introduction of scalar diffusivity coefficients into the mixing equation is found to be more justifiable in the natural coordinate system than in a rectangular Cartesian coordinate system. The transformed mixing equation unifies and generalizes essential concepts of several existing models which have been used successfully for simulating steady state transverse mixing in irregular natural channels. Solution methods, both analytical and numerical, and parameter estimation methods are presented, after which some results of simulation are compared with observed data.