References
- Gotoh H., Yasuda Y., Ohtsu I. Effect of channel slope on flow characteristics of undular hydraulic jumps. WIT Trans. Ecology Envir 2005:83:33–43.
- Chanson H. Flow characteristics of undular hydraulic jumps. Comparison with near-critical flows. Report CH 45/95. The University of Queensland, Australia, 1995.
- Riabenko O., Kliukha O., Halych O., Poplavskyi D. Impact of Undular Jump Characteristics on Erosion of Tailrace Channel. In: Blikharskyy Z. (ed). Proceedings of EcoComfort 2020. EcoComfort 2020. Lecture Notes in Civil Engineering. Springer, Cham. 2023:100. https://doi.org/10.1007/978-3-030-57340-9_44
- Riabenko O. A. Khvylʹovyy strybok: monohr. (Undular jump: monograph). Rivne: NUWEE, 2022. (In Ukrainian).
- Darcy H., Bazin H. Hydraulic research. Imprimerie impériale. Parts 1 and 2. (Imperial Printing Office. Parts 1 and 2). Paris, 1865. (In French)
- Bőss P. Berechnung des Grundwasserspiegels. (Calculation of the groundwater level). Forschungsarbeiten. Heft 284, NW7. Berlin, 1927. (In German)
- Bakhmetev B. A. O neravnomernom techenii zhidkosti v otkrytom kanale. (On non-uniform liquid flow in open channel). Leningrad: Kubuch, 1928. (In Russian)
- Sukhomel G. I. Gidravlika. (Hydraulics). Kyiv, 1933. (In Ukrainian)
- Krasnitskiy M. S. Khvyl’ovyy strybok. (Undular jump). Applied Mechanics, Department of Technical Sciences of the AS USSR 1955:1(2):235–238. (In Ukrainian)
- Iwasa Y. Undular jump and its limiting Condition for existence. Proc. 5th Japan National Congress for Applied Mechanics. Tokyo, 1955.
- Smyslov V. V. Teoriya plotiny s bol’shim podokonnikom. (Theory of weir with large sill). Kyiv: AN USSR, 1956. (In Russian)
- Jones L. E. Some observations on the undular jump. Proc. ASCE, HD. 1964:90(3):69–82. https://doi.org/10.1061/JYCEAJ.0001058
- Holtorf G. Wellensprung. (Undular jump). Water Management 1967:12:427–432. (In German)
- Tursunov A. A. Okolokriticheskoye sostoyaniye gravitatsionnykh potokov vody. (Near-critical state of gravity water flows). Izvestiya VNIIG 1969:90:201–224. (In Russian)
- Andersen V. M. Undular Hydraulic Jump. Journal of the Hydraulics Division. ASCE, 1978:104:1185–1188. https://doi.org/10.1061/JYCEAJ.0005048
- Hager W. H., Hutter K. On pseudo-uniform flow in open channel hydraulics. Acta Mechanica 1984:53(3–4):183–200. https://doi.org/10.1007/BF01177950
- Сhanson H., Montes J. S. Characteristics of undular hydraulic jumps. Experimental apparatus and flow patterns. J. Hydraul. Eng. 1995:121(2):129–144. https://doi.org/10.1061/(ASCE)0733-9429(1995)121:2(129)
- Ohtsu I., Yasuda Y., Gotoh H. Hydraulic condition for undular jump formation. Journal of Hydraulic Research 2001:39:203–209. https://doi.org/10.1080/00221680109499821
- Steinrűck H., Schneider W., Grillhofer W. A multiple scales analysis of the undular hydraulic jump in turbulent open channel flow. Fluid Dynamics Research 2003:41–45. https://doi.org/10.1016/S0169-5983(03)00041-8
- Grillhofer W. Wellenförmiger Sprung in der turbulenten Strömung eines Kanals mit freier Oberfläche. (Undular jump in turbulent flow of channel with free surface). Thesis. Vienna University of Technology, 2002. (In German)
- Lennon J. M., Hill D. F. Particle image velocity measurements of undular and hydraulic jumps. Journal of Hydraulic Engineering 2006:12831294. https://doi.org/10.1061/(ASCE)0733-9429(2006)132:12(1283)
- Bose S. K., Castro-Orgaz O., Dey S. Free surface profiles of undular hydraulic jumps. Journal of Hydraulic Engineering 2012:138(4):362–366. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000510
- Castro-Orgaz O., Chanson H. Free surface profiles of near-critical instabilities in open channel flows: undular hydraulic jumps. Environ Fluid Mech 2022:22:275–300. https://doi.org/10.1007/s10652-021-09797-3
- Langhi M., Hosoda T. Transition from undular jump to breaking jump. Journal of Hydraulic Research 2023:61(6):824–837. https://doi.org/10.1080/00221686.2023.2239188
- Castro-Orgas O. Weakly undular hydraulic jump: Effects of friction. Journal Hydraul. Res. 2010:48(4):453–465. https://doi.org/10.1080/00221686.2010.491646
- Ryabenko A. A. Conditions Favorable to the Existence of an Undulating Jump. Hydrotechnical Constraction 1990:24(12):762–770. https://doi.org/10.1007/BF01434602
- Favre H. Etude theorique et experimentale des ondes de translation dans les canaux de’couverts. (Theoretical and experimental study of translation waves in open channels). Dunod, 1935. (In French)
- Wiegel R. L. A Presentation of Cnoidal Wave Theory for Practical Application. J. Fluid Mech. 1960:1:273–286. https://doi.org/10.1017/S0022112060001481
- Gunko F. G. (Ed.). Gidravlicheskiye raschety konstruktsiy, upravleniye turbulentnost’yu potoka. Rekomendatsii po proyektirovaniyu. (Hydraulic calculations of structures, control of turbulence flow. Recommendations for designing). Leningrad. Energia 1974:110. (In Russian)
- Halych O. Improvement of methods for calculating the free-surface profile of undular jump with taking into account the energy losses and wave attenuation along the length. PhD thesis. Rivne, 2019.
- Riabenko O. A., Halych O. O., Poplavskiy D. M. Eksperymentalʹne doslidzhennya vil’noyi poverkhni blyz’kokrytychnykh techiy. (Experimental investigation of near-critical flows’ free-surface). Visnyk NUWEE 2015:3(71):94–99. (In Ukrainian)