Author(s): Bernhard H. Schmid
Linked Author(s):
Keywords: Solute transport; Transverse mixing; Mathematical model; Analytic solution
Abstract: In many industrialized countries water power development has resulted in chains of run-of-river plants operating on most of the major rivers and streams. Run-of-river impoundments are characterized by considerable longitudinal changes in waterdepth, usually much in excess of the 100% mark. Whereas, in densely populated areas, the impoundments are often flanked by backwater dikes which keep river width roughly constant, an assumption of constant water-depth is clearly not justified in these cases. This assumption of constant water-depth is, however, among the conditions required by currently available analytic solutions and easy-to-use formulae of (passive) transverse mixing, which throws considerable doubt on the applicability of these relationships and indicates the need for an engineering tool capable of dealing with longitudinally varying water-depths and flow velocities, resp. This paper presents an approximate model of passive solute transport and mixing in laterally confined run-of-river impoundments. In order to derive an analytic solution to the problem, a number of assumptions had to be made, which, however, do not impose conditions additional to those required for the (previous) solution to the constant depth case. In contrast to that, longitudinal variations in water-depths and flow velocities are accounted for. No particular functional form of the spatial waterdepth distribution is required, the analytic solution being general enough to deal with all relating mathematical expressions that can be integrated analytically (e. g. polynomials of arbitrary order). Finally, a description of a practical application of the newly derived solution to the Austrian Danube run-of-river impoundment Greifenstein is given. There, the model was used to answer the question of whether a particular water quality monitoring station, which (for technical reasons) had been installed close to the left bank, could be expected to detect pollutant spills originating from certain industrial estates on the opposite right bank. It was shown that, in such a case, water management decisions would most probably have to rely on other sources of information.
Year: 1999