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 convectiondiffusion (mixing) equation degived 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 numeri;:al, and parameter estimation methods are presented, after which some results of simulation are compared with observed data.

Dilution and volatilization of groundwater contaminant discharges in streams

“…Numerous studies propose theoretical equations to predict how the transverse diffusion coefficient varies with stream geometry and flow conditions (e.g., Bansal 1971;Yotsukura and Sayre 1976;Sanders et al 1977;Fischer et al 1979;Rutherford 1994;Jeon et al 2007), which can result in significantly different concentration distributions and mixing lengths. In fact only in-situ tracer tests can reliably estimate this parameter, but these are logistically difficult and expensive.…”

An Approach to the Study of Transverse Mixing in Streams

“…that of the cumulative discharge method (20) and naturally the accuracy of model results essentially depends on the available knowledge of velocity distribution and dispersion coefficient for the river stretch considered (the application part of this paper involves some information in this respect).…”

“…1 ay my (2) This is the familiar, two-dimensional equation of turbulent dispersion (c.f. Yotsukara and Sayre [20]). Here c is concentration, vx and v:Y are the local velocity components, Dy is the local dispersion coefficient, h the local now depth, while mx and my are the metric coefficients.…”

“…In most of the cases steady flow and pollutant release can be also assumed. All these assumptions allow description of the mixing process by the two-dimensional, steady-state equation of turbulent dispersion as it was done by Holley [4], Yctsukara and Sayre (20] and others.…”

“…These have prompted Fischer to introduce the stream tube concept [3], (11), (19], Yotsukara and Cobb (18] the cumulative discharge, Chang [2], Yotsukara and Sayre (20], further Somlyody (13] the orthogonal, curvilinear system of coordinates following the bend conditions. Further modification was suggested by Somlyody [15] upon introducing the stream-lines of the mass density vector field, the concept and equations of the mass streamline.…”