Author(s): Benoit Cushman-Roisin; George S. Constantinescu

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Keywords: Hydraulic models; hydraulic resistance; one-dimensional models; shallow flows; streams and rivers

Abstract: We consider the dynamic adjustment between two streams past their confluence. Lateral mixing is ignored because it is significant only on longer distances. The theory predicts an exponential decay of the difference between the two stream velocities, starting from the point of confluence. Velocity equalization proceeds with the Bernoulli function of each stream decreasing under the action of bottom friction, more so for the faster flow than for the slower flow. The faster stream slows down and, to conserve flowrate, expands laterally, thus squeezing the slower stream, which accelerates, to conserve its flowrate. Thus, the faster stream decelerates while the slower stream accelerates, and the line demarcating the two streams migrates laterally toward the side of the lower velocity. This proceeds until both stream achieve equal velocities. Agreement between theory and data from both laboratory experiments and numerical simulations confirms that lateral mixing is not the mechanism controlling velocity equalization.

DOI: https://doi.org/10.1080/00221686.2019.1573765

Year: 2020