Relationships between river dune parameters when approximating their longitudinal profile by a triangle

The subject of the study is the geometric characteristics of river bed forms, the knowledge of which is important for solving a number of river hydraulics problems, in particular for determining the hydraulic resistance of the channel. It should be noted that many researchers consider that its value depends on the steepness of the river dunes. At the same time, there is a lot of data indicating that in addition to the dune steepness, the shape of the longitudinal relief of the bed forms, namely, the location of the crest of the dune relative to its troughs, also influences the value of hydraulic resistance. In order to take this circumstance into account, the notion of the dune asymmetry coefficient and the notion of the wetted perimeter of the dune are introduced. The application of the possibility of approximating the longitudinal profile of the dune by a triangle has allowed us to match the main elements of the triangle with the parameters of river dunes normally used in studies of the fluvial process. Since the triangle elements are connected by well-known geometric and trigonometric relations, the proposed approximation allows us to analytically derive dependences between the main parameters characterising river dunes. For clarity, the obtained relationships are presented not only in the form of formulae, but also in the form of graphs and tables. Although the task of extensive verification of the deduced relations by actual data is not set in the present paper, the obtained dependences are in good agreement with some results of statistical processing of data from field and laboratory researches given in the literature on river hydraulics, which confirms the admissibility of approximating the dune shape by a triangle and the possibility of using the deduced relationships as at least an approximate assessment of the quantitative values of the main river dune parameters.

1. Gladkov, Gennadii L. and Pachom V. Beljakov. “Sediment transport in rivers: dependence of the dunes parameters on the determining factors.” Vestnik Gosudarstvennogo universiteta morskogo i rechnogo flota imeni admirala S. O. Makarova 13.1 (2021): 52–63. DOI: 10.21821/2309-5180-2021-13-1-52-63.

2. Scheiber, L., and A. Lefebvre. “The influence of geometric definitions on dune characteristics.” MARID VII. Seventh International Conference on Marine and River Dune Dynamics. Rennes, France, 3–5 April 2023. 2023. 293–297.

3. Gutierrez, Ronald R., Jorge D. Abad, Daniel R. Parsons, and James L. Best. “Discrimination of bed form scales using robust spline filters and wavelet transforms: Methods and application to synthetic signals and bed forms of the Río Paraná, Argentina.” Journal of Geophysical Research: Earth Surface 118.3 (2013): 1400–1418. DOI: 10.1002/jgrf.20102.

4. Van Rijn, Leo C. “Sediment transport, part III: bed forms and alluvial roughness.” Journal of hydraulic engineering 110.12 (1984): 1733–1754. DOI: 10.1061/(ASCE)0733–9429(1984)110:12(1733).

5. Znamenskaya, N. S. Gryadovoe dvizhenie nanosov. Teoriya i prakticheskie prilozheniya. L.: Gidrometeorologicheskoe izdatel’stvo, 1968.

6. Cisneros, Julia, Jim Best, Thaienne van Dijk, Renato Paes de Almeida, Mario Amsler, Justin Boldt, Bernardo Frietas, Cristiano Galeazzi, Rick Huizinga, Marco Ianniruberto, Hongbo Ma, Jeff Nittrouer, Kevin Oberg, Oscar Orfeo, Dan Parsons, Ricardo Szupiany, Ping Wang, and Yuanfeng Zhang. “Dunes in the world’s big rivers are characterized by low-angle lee-side slopes and a complex shape.” Nature Geoscience 13.2 (2020): 156–162. DOI: 10.1038/s41561-019-0511-7.

7. Baryshnikov, N. B. Dinamika ruslovykh potokov. SPb.: izd. RGGMU, 2007.

8. Shinohara, Kinji, and Toichiro Tsubaki. “On the characteristics of sand waves formed upon the beds of the open channels and rivers.” Reports of Research Institute for Applied Mechanics 7.25 (1959): 15–45.

9. Swart, Dirk H. “Predictive equations regarding coastal transports.” Proceedings of the Fifteenth Conference on Coastal Engineering. Vol. II. American Society of Civil Engineers, 1976. Pp. 1113–1132. DOI: 10.1061/9780872620834.066.

10. Lefebvre, Alice, Andries J. Paarlberg, and Christian Winter. “Characterising natural bedform morphology and its influence on flow.” Geo-marine letters 36 (2016): 379–393. DOI: 10.1007/s00367-016-0455-5.

11. Wu, Shuaihu, Y. Jun Xu, Bo Wang, and Heqin Cheng. “Riverbed dune morphology of the Lowermost Mississippi River–Implications of leeside slope, flow resistance and bedload transport in a large alluvial river.” Geomorphology 385 (2021): 107733. DOI: 10.1016/j.geomorph.2021.107733.