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Transverse Mixing Coefficients in Non-Uniform Flows: Laboratory Experiments

Author(s): Clement Fagour; Lorris Gond; Jerome Le Coz; Nicolas Riviere; Louis Gostiaux; Emmanuel Mignot; Lylia Kateb

Linked Author(s): Nicolas Riviere, Emmanuel Mignot

Keywords: Mixing; Pollution; River; Laboratory; Uniformity; Acceleration

Abstract: The value of the transverse mixing coefficient in a river reach is of major importance for river management. It quantifies the capacity of a pollutant cloud to spread over the channel width. The coefficient value depends on the flow characteristics and the channel geometry. It has been quantified by many authors for more than 70 years in rivers and laboratory studies in order to establish empirical predictive formulations. However, if laboratory studies could impose a uniform flow condition, the field studies only assumed this flow uniformity and ignored the possible flows streamwise variations. The measured coefficients and related adjusted empirical equations are thus useful for rivers in lowland areas but not to piedmont rivers where the mean flow velocity can strongly vary over short streamwise distances. For instance, in the Durance River, a gravel-bedded river in the French Alps, recent measurements reported that the transverse mixing coefficient varies strongly over very short distances, and the authors attributed this variation to the flow non-uniformity, which they quantified through a new parameter labeled κ. To the best of our knowledge, transverse mixing coefficients in laboratory channels were quantified only for uniform flows. In order to verify the influence of flow non-uniformity, we recently performed tracing experiments in a straight flume for both uniform flows and accelerating flows over a forward-facing step with a gentle upward slope. The methodology applied to estimate the transverse mixing coefficient was similar to most studies available in the literature, the only innovative aspect was its application to a non-uniform flow. For each flow, a controlled discharge of salted water, which density was corrected to unity by adding alcohol, was continuously released in the upstream part of a straight flume with constant slope and cross-section. Several conductivity probes, daily calibrated and fixed to an automated displacement carriage, were then moved along several cross-sections further downstream. As expected, the salt concentration profiles fairly fitted Gaussian curves, with increasing variance towards downstream. The quantification of the variance increasing rate then permitted to quantify the transverse mixing coefficient for both uniform and accelerating flows. The coefficients obtained in uniform flows agree well with the estimations from empirical laws available in the literature, but those measured in the accelerating flows strongly exceed these correlations. These results thus confirm the recent field observations. Moreover, these transverse mixing coefficients appear to correlate well with the non-uniform parameter κ. These results should thus be of major interest for river managers aiming to predict the spreading of pollution or industrial releases in piedmont rivers.

DOI: https://doi.org/10.3850/IAHR-39WC252171192022674

Year: 2022

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