Hidrológiai Közlöny 1977 (57. évfolyam)

2. szám - Dr. Somlyódy László: A Duna Szob és Budapest közötti szakaszára vonatkozó, leíró jellegű vízminőségi (diszperziós) modell kidolgozása

78 Hidrológiai Közlöny 1977. 2. sz. Dr. Somlyódi L.: A Duna Szob és Budapesti közötti szakasza the transverse changes (

Fig. 2), which were in general more pronounced than the longitudinal ones, further the slow rate of mixing (as indicated by the estimated effect of the tributary Vág River, which has also been entered in the figure); difficulty in adopting the critical component; the uncleared impacts of future barrages; the small number of observation data; The way to be followed was thus largely unknown. The approach which appeared most feasible consisted of starting simultaneous studies on several processes, in several directions and of formulating several submodels for these. The combination thereof was expected to yield the eventual water quality model, further the parameter, or parameters to be reproduced. The first sub-, or basic model is the dispersion model, since the slow rate of mixing presents radical differences with respect to the streams studied thus far. In keeping with earlier experiences the dispersion model is descriptive in character, applies to the steady case, is two-dimensional and involves integral means along verticals. The differential equation —Eq. (I) — adopted as the starting basis is of the parabolic type. The problem is one of initial- and boundary values (2), In formulating the modi J equations written in a curvilinear set of coordinates (Fig. 3) and based on the concept of mass current lines have been adopted (Fig. 5) (4), (5), (2<t), (3a). These can be used for • determining the variations in background pollution, as well as for studying individual polluting discharges. In the latter case the principle of superiinposement has been applied, so that the number of discharges is theoretically unlimited. The numerical method developed for solving the equations forms a transition between the methods of finite differences and finite elements, but involves also features akin to the relative diffusion model. The computation is performed using implicite schemes which are of the fourth order transversally and of the second order longitudinally. The result yields besides the field of concentration also the coordinates of the mass current lines, the latter presenting a geometrical picture on mixing. The organization of the model corresponds to the Hungarian filing system of river data. As a first steep the edge of the stream (plan view) was produced at a particular stage. This involved information on the centerline, channel data and surface profile of the stream. The latter may be derived from direct observations or from a one-dimensional hydraulic model. The language FORTRAN IV has been used for programming the dispersion model. Besides the data listed in the foregoing, the distributions of velocity, the initial conditions and the dispersion coefficients are needed for using the model. The velocity distributions have been determined by field measurements and computed by empirical relations founded on the latter. The initial conditions have, in general, also been determined by field measurements, or the locations and intensities of sources regarded as concentrated were given. The magnitude of the dispersion coefficient is determined preferably by tracer observations, which are then used in selecting one of the expressions published in the professional literature. The formula of Elder [7] has been checked for correctness. In the Vác Danube arm measurements have been performed at two different streamflow rates, downstream of the Standard Cross-Section No. 7. The tracer introduced at a steady rate as a point source was Na-fluoresceine. Samples were retrieved from three crosssections. In each of nine verticals thenumber of sampling points was five. Each measurement has been photographed from the air (Fig. 6), testing also photographic equipment using several colour bands. The samples have been analysed for their fluorescein!', content by a Pye Unicam spectrophotometer. From the distributions of concentration (Fig. 7) the dispersion coefficient has been determined by several different methods. The values obtained agreed to order of magnitude with the results of earlier measurements and the shape of the curve followed closely the one found using the formula of Elder. The value of y may be estimated at 0.13 (Fig. 8). The use of Eq. (7) is thus considered reliable enough. Further observations may be indicated to study the value of y. The use of the model has been demonstrated for the Szob — Nagymaros section. The COD distribution shown in Fig. 2 has been adopted as the initial condition at a streamflow rate of 1400 cu.m/see. The computed water edge of the stream and the distribution of concentration in the Nagymaros cross-section, together with the dimensions are shown in Figs. !) and 10, respectively. From the results the following conclusions have been arrived at

: a ) Owing to the rather wide spacing of the standard V. O. cross-seetions the stream cannot be reproduced accurately in the model. More closely spaced channel data would be needed for describing effects of local character. b

) Mixing occurs at a very slow rate only, the mass current lines being essentially the same as the streamlines. The water body more highly polluted under the influence of the Vág River remains along the left-hand bank over the entire length of the section. c

) The distribution observed would imply a mixing intensity higher than that computed by the model. This may be traced back to several causes, such as differences between the actual- and computed water edges, the simplified velocity field, secondary currents, errors of measurement, etc., but these influences may be subject to subsequent studies. The part-model described here must not be regarded yet a definite one. Further refinement, final verification and sensitivity testing of the model will present task of the future. The combination with the one-dimensional hydraulic model, as well as allowance for the effect of assimilation processes may also be attempted at a later date.