INFLUENCE OF THE CHANNEL ALLUVIUM PROPERTIES ON THE GEOMETRIC CHARACTERISTICS OF BOTTOM DUNES

The paper demonstrates that not all combinations of steepness and asymmetry parameters of riverbed dunes ensure their morphological stability. By comparing the “triangular” approximation describing the dune profile as a triangle and the dune profile approximation using a “sinusoidal” model (constructed by gluing two branches of a modified sinusoid), the influence of the approximation method choice on the permissible ranges of dune steepness and asymmetry parameter ratios is analyzed. It is established that the requirement of firstderivative continuity (profile smoothness) at the trough and crest points, implemented in the “sinusoidal” model, imposes stricter constraints on dune geometry. It is shown that the maximum local slope of the back slope in the sinusoidal profile significantly exceeds the average slope of the corresponding triangular model. Based on the condition that the dune surface inclination angle must not exceed the angle of repose of the material from which the dune is composed, analytical relationships are derived to determine the critical steepness and critical asymmetry for “triangular” and “sinusoidal” dunes. Combined stability nomograms are constructed, enabling identification of zones with physically impossible parameter combinations for various types of bed sediments. The results can be used to verify bathymetric survey data and improve calculations of channel hydraulic resistance.

1. Abraham D., Kuhnle R., and Odgaard J.A. Validation of Bed-Load Transport Measurements with Time-Sequenced Bathymetric Data. J. Hydraul. Eng. 2011.137:723-728. DOI: 10.1061/(ASCE)HY.1943-7900.0000357.

2. Baryshnikov N.B. Dynamics of channel flows. St. Petersburg: RSHU Publ., 2007. 314 p. (in Russ.)

3. Ferguson, R., Lewin, J., and Hardy, R. (2022). Fluvial processes and landforms. Geological Society, London, Memoirs. 58. M58-2021. 10.1144/M58-2021-18.

4. Gutierrez, R. R., Abad, J. D., Parsons, D. R., and Best, J. L. (2013). Discrimination of bed form scales using robust spline filters and wavelet transforms: Methods and application to synthetic signals and bed forms of the Ro Parana, Argentina. Journal of Geophysical Research: Earth Surface, 118(3):1400-1418.

5. Kostyuchenko A.A., Zavarzin R.V. A method for performing and processing measurements to determine bedform parameters // Vodnye puti i ruslovye protsessy. Gidrotekhnicheskie sooruzheniya vodnykh putey: Sbornik nauchnykh trudov [Waterways and channel processes. Hydraulic structures of waterways: Collection of scientific papers]. Issue 6, Part 1. St. Petersburg: Admiral Makarov University, 2023. P. 151–165 (in Russ.)

6. Leary K.C.P. Estimating sand bed load in rivers by tracking dunes: a comparison of methods based on bed elevation time series / K.C.P. Leary, D. Buscombe // Earth Surface Dynamics. – 2020. – Vol. 8. – 13 p

7. Libina N.V. Methods for processing and analyzing digital bottom relief models // Okeanologiya. 2022. Vol. 62. No. 2. P. 324–333. DOI: 10.31857/S0030157422020125 (in Russ.)

8. Nuñez-Gonzalez, F., Hesse, D., Ettmer, B., Kume, E., and Link, O. (2014). Objective method for ranking bedforms with a 3-dimensionality-index, in: River Flow 2014, p. 1059-1065.

9. Samsonov T.E. Cartographic methods of visualization and generalization of digital terrain models. Modern methods and technologies of digital terrain modeling in Earth sciences // Sovremennye metody i tekhnologii tsifrovogo modelirovaniya rel’efa v naukakh o Zemle. Iss. 6. 2016. P. 9–18 (in Russ.)

10. Schippa, L. and Cavalieri, I. (2021). Semiautomatic algorithm for the interpretation of the bedforms and statistical analysis. 169-179. DOI: 10.2495/WRM210151

11. Shinohara K. On the Characteristics of Sand Waves Formed upon Beds of the Open Channels and Rivers / K. Shinohara, T. Tsubaki // Reports of Research Institute for Applied Mechanics. – 1959. – Vol. VII. – No. 25. – P. 15–45.

12. Sidorchuk A. Estimation of bedload transport in a river channel considering data on active and passive bedform dynamics // Vodnye resursy [Water Resources]. 2015. Vol. 42. No. 1. P. 31–44. DOI: 10.7868/S0321059615010137 (in Russ.)

13. Simons, D., Richardson, E., and Nordin, C., 1965, Bedload equation for ripples and dunes: U.S. Geological Survey Professional Paper 462, p. H1-H9, DOI: 10.3133/pp462H

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

15. Van Denderen, R. P., Schielen, R. M. J., Paarlberg, A. J., Reneerkens, M., and Augustijn, D. C. M. (2024). Analyzing natural bed-level dynamics to mitigate the morphological impact of river interventions. River Research and Applications, 40(5), 735–746. DOI: 10.1002/rra.4270

16. Van Rijn L. C. Sediment transport, part III: bed forms and alluvial roughness / L. C. Van Rijn // Journal of hydraulic engineering. – 1984. – Vol. 110. No. 12. P. 1733–1754. DOI: 10.1061/(ASCE)0733–9429(1984)110:12(1733).

17. Yalin M.S. Mechanics of Sediment Transport. Pergamon Press, Oxford, 1977.

18. Zamyshlyaev V.I. Relationships between river dune parameters when approximating their longitudinal profile by a triangle // Vestnik Gosudarstvennogo universiteta morskogo i rechnogo flota imeni admirala S.O. Makarova. 2024. Vol. 16. No. 2. P. 236–250. DOI: 10.21821/2309-5180-2024-16-2-236-250 (in Russ.)

19. Zamyshlyaev V.I. Approximation of the longitudinal profile of river dunes using sine wave branches. 2026 (in print) (in Russ.)

20. Znamenskaya N.S. Bedform-related sediment transport. Theory and practical applications. Leningrad: Gidrometeoizdat, 1968. 188 p. (in Russ.)