This work is licensed under the Creative Commons Attribution 4.0 International License.
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.Search in Google Scholar
Chanson H. Flow characteristics of undular hydraulic jumps. Comparison with near-critical flows. Report CH 45/95. The University of Queensland, Australia, 1995.Search in Google Scholar
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_44Search in Google Scholar
Riabenko O. A. Khvylʹovyy strybok: monohr. (Undular jump: monograph). Rivne: NUWEE, 2022. (In Ukrainian).Search in Google Scholar
Darcy H., Bazin H. Hydraulic research. Imprimerie impériale. Parts 1 and 2. (Imperial Printing Office. Parts 1 and 2). Paris, 1865. (In French)Search in Google Scholar
Bőss P. Berechnung des Grundwasserspiegels. (Calculation of the groundwater level). Forschungsarbeiten. Heft 284, NW7. Berlin, 1927. (In German)Search in Google Scholar
Bakhmetev B. A. O neravnomernom techenii zhidkosti v otkrytom kanale. (On non-uniform liquid flow in open channel). Leningrad: Kubuch, 1928. (In Russian)Search in Google Scholar
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)Search in Google Scholar
Iwasa Y. Undular jump and its limiting Condition for existence. Proc. 5th Japan National Congress for Applied Mechanics. Tokyo, 1955.Search in Google Scholar
Smyslov V. V. Teoriya plotiny s bol’shim podokonnikom. (Theory of weir with large sill). Kyiv: AN USSR, 1956. (In Russian)Search in Google Scholar
Jones L. E. Some observations on the undular jump. Proc. ASCE, HD. 1964:90(3):69–82. https://doi.org/10.1061/JYCEAJ.0001058Search in Google Scholar
Holtorf G. Wellensprung. (Undular jump). Water Management 1967:12:427–432. (In German)Search in Google Scholar
Tursunov A. A. Okolokriticheskoye sostoyaniye gravitatsionnykh potokov vody. (Near-critical state of gravity water flows). Izvestiya VNIIG 1969:90:201–224. (In Russian)Search in Google Scholar
Andersen V. M. Undular Hydraulic Jump. Journal of the Hydraulics Division. ASCE, 1978:104:1185–1188. https://doi.org/10.1061/JYCEAJ.0005048Search in Google Scholar
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/BF01177950Search in Google Scholar
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)Search in Google Scholar
Ohtsu I., Yasuda Y., Gotoh H. Hydraulic condition for undular jump formation. Journal of Hydraulic Research 2001:39:203–209. https://doi.org/10.1080/00221680109499821Search in Google Scholar
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)00041-8Search in Google Scholar
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)Search in Google Scholar
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)Search in Google Scholar
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.1943-7900.0000510Search in Google Scholar
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/s10652-021-09797-3Search in Google Scholar
Langhi M., Hosoda T. Transition from undular jump to breaking jump. Journal of Hydraulic Research 2023:61(6):824–837. https://doi.org/10.1080/00221686.2023.2239188Search in Google Scholar
Castro-Orgas O. Weakly undular hydraulic jump: Effects of friction. Journal Hydraul. Res. 2010:48(4):453–465. https://doi.org/10.1080/00221686.2010.491646Search in Google Scholar
Ryabenko A. A. Conditions Favorable to the Existence of an Undulating Jump. Hydrotechnical Constraction 1990:24(12):762–770. https://doi.org/10.1007/BF01434602Search in Google Scholar
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)Search in Google Scholar
Wiegel R. L. A Presentation of Cnoidal Wave Theory for Practical Application. J. Fluid Mech. 1960:1:273–286. https://doi.org/10.1017/S0022112060001481Search in Google Scholar
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)Search in Google Scholar
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.Search in Google Scholar
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)Search in Google Scholar