Formulas for estimating the effects exerted by a bore and a solitary wave on a partially immersed structure, obtained by approximating the results of numerical simulations
https://doi.org/10.59887/2073-6673.2025.18(4)-9
EDN: UZNWKF
Abstract
This study derives analytical formulas for estimating the loads exerted by a bore and a solitary wave on a fixed, partially immersed body. These estimates are required in the design and operation of coastal structures. The formulas are obtained by fitting results from extensive numerical simulations spanning variations in body submergence, body length, and incident-wave amplitude. We consider runup heights on the front and back sides of the body, as well as the horizontal and vertical components of the resultant wave force. The bore and solitary-wave problems are solved using one-dimensional shallow water models based on the first and second long-wave approximations, respectively. We report the average and maximum relative errors of the formulas and compare their predictions with results from previous studies. These comparisons demonstrate that the proposed formulas are applicable across the parameter ranges considered.
Keywords
solitary wave,
vertical bore,
partially immersed structure,
shallow water,
nonlinear dispersion,
numerical algorithm,
data fitting
Supporting agencies: The research was carried out within the state assignment of Ministry of Science and Higher Education of the Russian Federation for Federal Research Center for Information and Computational Technologies.
About the Authors
O. I. Gusev
Federal Research Center for Information and Computational Technologies
Russian Federation
Russian Federation
WoS ResearcherID: Р-2157-2015, Scopus AuthorID: 56779732800
6 Academician M.A. Lavrentiev Ave., Novosibirsk, 6630090
G. S. Khakimzyanov
Federal Research Center for Information and Computational Technologies
Russian Federation
Russian Federation
WoS ResearcherID: Р-5004-2016, Scopus AuthorID: 6603081316
6 Academician M.A. Lavrentiev Ave., Novosibirsk, 6630090
V. S. Skiba
Federal Research Center for Information and Computational Technologies
Russian Federation
Russian Federation
WoS ResearcherID: AEG-9551-2022, Scopus AuthorID: 58064951300
6 Academician M.A. Lavrentiev Ave., Novosibirsk, 6630090
L. B. Chubarov
Federal Research Center for Information and Computational Technologies
Russian Federation
Russian Federation
WoS ResearcherID: Р-8247-2015, Scopus AuthorID: 6603063050
6 Academician M.A. Lavrentiev Ave., Novosibirsk, 6630090
References
1. Mei CC, Black JL. Scattering of surface waves by rectangular obstacles in waters of finite depth. Journal of Fluid Mechanics. 1969;38:499–511. https://doi.org/10.1017/S0022112069000309
2. Fang Q, Guo A. Analytical and experimental study of focused wave action on a partially immersed box. Mathematical Problems in Engineering. 2019;2019:9850302. https://doi.org/10.1155/2019/9850302
3. Kamynin EY, Maximov VV, Nudner IS, Semenov KK, Khakimzyanov GS. Study of interaction of the solitary wave with a partially submerged stationary construction. Fundamental and Applied Hydrophysics. 2010;(4):39–54. URL: https://hydrophysics.spbrc.ru/jour/article/view/1005 (date of access: 01.08.2025) (In Russ)
4. Lu X, Wang KH. Modeling a solitary wave interaction with a fixed floating body using an integrated analytical numerical approach. Ocean Engineering. 2015;109:691–704. https://doi.org/10.1016/j.oceaneng.2015.09.050
5. Nudner IS, Semenov KK, Khakimzyanov GS, Shokina NY. Investigations of the long marine waves interaction with the structures protected by the vertical barriers (In Russ). Fundamental and Applied Hydrophysics. 2017;10(4):31–43. URL: https://hydrophysics.spbrc.ru/jour/article/view/1118 (date of access: 01.08.2025)
6. Park JC, Kim MH, Miyata H. Three-dimensional numerical wave tank simulations on fully nonlinear wave current body interactions. Journal of Marine Science and Technology. 2001;6(2):70–82. https://doi.org/10.1007/s773-001-8377-2
7. Orzech MD, Shi F, Veeramony J, Batty J, Calantoni J, Kirby JT. Incorporating floating surface objects into a fully dispersive surface wave model. Ocean Modelling. 2016;102:14–26. https://doi.org/10.1016/j.ocemod.2016.04.007
8. Lin P. A multiple-layer σ-coordinate model for simulation of wave structure interaction. Computers & Fluids. 2006;35(2):147–167. https://doi.org/10.1016/j.compfluid.2004.11.008
9. Chang CH. Study of a solitary wave interacting with a surface piercing square cylinder using a three-dimensional fully nonlinear model with grid-refinement technique on surface layers. Journal of Marine Engineering & Technology. 2017;16(1):22–36. http://dx.doi.org/10.1080/20464177.2016.1277605
10. Ma Y, Yuan C, Ai C, Dong G. Comparison between a non-hydrostatic model and OpenFOAM for 2d wave-structure interactions. Ocean Engineering. 2019;183:419–425. https://doi.org/10.1016/j.oceaneng.2019.05.002
11. Sun JL, Wang CZ, Wu GX, Khoo BC. Fully nonlinear simulations of interactions between solitary waves and structures based on the finite element method. Ocean Engineering. 2015;108:202–215. https://doi.org/10.1016/j.oceaneng.2015.08.007
12. Chang CH, Wang KH, Hsieh PC. Fully nonlinear model for simulating solitary waves propagating through a partially immersed rectangular structure. Journal of Coastal Research. 2017;33(6):1487–1497. https://doi.org/10.2112/JCOASTRES-D-16-00061.1
13. Gusev OI, Khakimzyanov GS, Chubarov LB. Numerical investigation of the wave force on a partially immersed rectangular structure: Long waves over a flat bottom. Ocean Engineering. 2021;221:108540. https://doi.org/10.1016/j.oceaneng.2020.108540
14. Liu PLF, Al-Banaa K. Solitary wave runup and force on a vertical barrier. Journal of Fluid Mechanics. 2004;505:225– 233. https://doi.org/10.1017/S0022112004008547
15. Dorfman AA, Pechenin SA, Semenov KK, Nudner IS, Maximov VV. Tsunami wave impact on marine hydrotechnical structures and coastal objects. Fundamental and Applied Hydrophysics. 2017;10(4):16–30. URL: https://hydrophysics.spbrc.ru/jour/article/view/1116 (date of access: 11.07.2025) (In Russ).
16. Gusev OI, Skiba VS, Khakimzyanov GS, Chubarov LB. Numerical study of the effect of long surface waves on a stationary partially immersed structure. In: Proceedings of All-Russian Conference “Advanced Technologies of Hydroacoustics and Hydrophysics”. St. Petersburg: POLYTECH-PRESS; 2024. p. 197–200.
17. Gusev OI, Khakimzyanov GS, Skiba VS, Chubarov LB. Shallow water modeling of wave structure interaction over irregular bottom. Ocean Engineering. 2023;267:113284. https://doi.org/10.1016/j.oceaneng.2022.113284
18. Khakimzyanov G, Dutykh D, Gusev O, Shokina NY. Dispersive shallow water wave modelling. Part II: Numerical simulation on a globally flat space. Communications in Computational Physics. 2018;23(1):30–92. https://doi.org/10.4208/cicp.OA-2016-0179b
19. Khakimzyanov G, Dutykh D. Long wave interaction with a partially immersed body. Part I: Mathematical models. Communications in Computational Physics. 2020;27(2):321–378. https://doi.org/10.4208/cicp.OA-2018-0294
20. Gusev OI, Skiba VS, Khakimzyanov GS, Chubarov LB. Influence of bottom roughness on the solitary-wave interaction with partially immersed rectangular body. Journal of Applied Mechanics and Technical Physics. 2023;64(1):50–63. https://doi.org/10.1134/S0021894423010066
21. Khakimzyanov G, Dutykh D, Fedotova Z, Gusev O. Dispersive Shallow Water Waves: Theory, Modeling, and Numerical Methods. Cham: Birkhäuser; 2020. 284 p. (Lecture Notes in Geosystems Mathematics and Computing). https://doi.org/10.1007/978-3-030-46267-3
22. Khakimzyanov G, Dutykh D, Gusev O. Longwave interaction with a partially immersed body. Part II: Numerical results [preprint]. arXiv. 2022. arXiv:2204.08210. Published online April 18, 2022. https://doi.org/10.48550/arXiv.2204.08210
23. Virtanen P, Gommers R, Oliphant TE, et al. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nature Methods. 2020;17:261–272. https://doi.org/10.1038/s41592-019-0686-2
24. Gusev OI, Skiba VS, Khakimzyanov GS, Chubarov LB. Numerical modeling of the impact of steep waves on partially immersed structures. Bulletin of Bashkir University. 2022;27(3):496–501 (In Russ). https://doi.org/10.33184/bulletin-bsu-2022.3.1
25. Stoker JJ. Water Waves: The Mathematical Theory with Applications. New York: Interscience Publishers; 1957. https://doi.org/10.1002/9781118033159
26. Byatt-Smith JGB. An integral equation for unsteady surface waves and a comment on the Boussinesq equation. Journal of Fluid Mechanics. 1971;49(3):625–633. https://doi.org/10.1017/S0022112071002295
27. Su CH, Mirie RM. On head-on collisions between two solitary waves. Journal of Fluid Mechanics. 1980;98(3):509–525. https://doi.org/10.1017/S0022112080000262
28. Maxworthy T. Experiments on collisions between solitary waves. Journal of Fluid Mechanics. 1976;76(1):177–186. https://doi.org/10.1017/S0022112076003194
29. Zagryadskaya NN, Ivanova SV, Nudner IS, Shoshin AI. Action of long waves on a vertical obstacle. Bulletin of VNIIG. 1980;138:94–101 (In Russ).
30. Manoylin SV. Some experimental and theoretical methods of estimation of tsunami wave action on hydro-technical structures and seaports. Technical Report 5. Krasnoyarsk: Siberian Branch of Computing Center; 1989 (In Russ).
31. Davletshin VH. Force action of solitary waves on vertical structures. In: Tsunami Meeting. Gorky: Institute of Applied Physics; 1984:41–43 (In Russ).
32. Chan RKC, Street RL. A computer study of finite-amplitude water waves. Journal of Computational Physics. 1970;6(1):68– 94. https://doi.org/10.1016/0021-9991(70)90005-7
33. Cooker MJ, Weidman PD, Bale DS. Reflection of a high-amplitude solitary wave at a vertical wall. Journal of Fluid Mechanics. 1997;342:141–158. https://doi.org/10.1017/S002211209700551X
34. Fenton JD, Rienecker MM. A Fourier method for solving nonlinear water-wave problems: application to solitary-wave interactions. Journal of Fluid Mechanics. 1982;118:411–443. https://doi.org/10.1017/S0022112082001141
35. Chen YH, Wang KH. Experiments and computations of solitary-wave interaction with fixed, partially submerged, vertical cylinders. Journal of Ocean Engineering and Marine Energy. 2019;5(2):189–204. https://doi.org/10.1007/s40722-019-00137-8
36. Ministry of Construction of Russia. SP 292.1325800.2017. Buildings and Structures in Tsunami-Prone Areas. Design Rules. Approved by Order No. 915/pr of June 23, 2017. Moscow: Standartinform; 2018:91 p. (In Russ).
Review
For citations:
Gusev O.I., Khakimzyanov G.S., Skiba V.S., Chubarov L.B. Formulas for estimating the effects exerted by a bore and a solitary wave on a partially immersed structure, obtained by approximating the results of numerical simulations. Fundamental and Applied Hydrophysics. 2025;18(4):120-137. https://doi.org/10.59887/2073-6673.2025.18(4)-9. EDN: UZNWKF
Views:
48
Email this article 