Three-dimensional phase-resolving surface wave model for finite depth
https://doi.org/10.59887/2073-6673.2025.18(1)-2
Abstract
The paper presents modification of the three-dimensional phase-resolving FWM (Full Wave Model) model of potential waves to simulate the evolution of waves on finite depth water and to determine the range of applicability of the proposed model. Calculations have been carried out to illustrate the fulfillment of the dispersion relation for waves in finite depth, initially assigned by JONSWAP spectrum. The quasi-stationary regime is considered. Calculations were carried out for two resolution options (almost one-dimensional and multidirectional waves) and for various dimensionless depth values. The agreement between theoretical and model calculations of the dispersion relation is shown with a sufficient accuracy on the base of calculated statistic characteristics. The proposed modification of the model is applicable for simulating the multimode wave field for a depth of no less than 0.1 of the maximum wavelength, which significantly expands the field of its application.
Keywords
wind waves,
phase-resolving modeling,
finite depth,
phase velocity,
dispersion relation,
three-dimensional wave modeling
Supporting agencies: The study was carried out within the framework of the Shirshov Institute of Oceanology state assignment (theme No. FMWE-2024-0028).
About the Author
K. V. Fokina
Shirshov Institute of Oceanology, Russian Academy of Sciences
Russian Federation
Russian Federation
36 Nakhimovsky Prosp., Moscow 117997
Scopus AuthorID: 57225150215
References
1. Young I.R., Babanin A.V. The form of the asymptotic depth-limited wind-wave spectrum: part II — the wavenumber spectrum. Coastal Engineering. 2009;56(5‒6):534‒542. doi:10.1016/j.coastaleng.2008.11.005
2. Bouws E., Günther H., Rosenthal W., et al. Similarity of the wind wave spectrum in finite depth water: 1. Spectral form. Journal of Geophysical Research Oceans. 1985;90(C1):985‒986. doi:10.1029/JC090iC01p00975
3. Bouws E., Günther H., Rosenthal W., et al. Similarity of the wind wave spectrum in finite depth water part 2: Statistical relations between shape and growth stage parameters. Deutsche Hydrografische Zeitschrift. 1987;40(1):1‒24. doi:10.1007/BF02328530
4. Eyhavand A., Peyman B. Experimental study on the growth and conversion of duration- and fetch-limited wind waves in water of finite depth. Ocean Engineering. 2022;26. doi:10.1016/j.oceaneng.2022.113020
5. Young I. The growth rate of finite depth wind-generated waves. Coastal Engineering. 1997;32(2):181–195. doi:10.1016/S0378-3839(97)81749-8
6. Young I. Wind Generated Ocean Waves. Elsevier Science; 1999. 288 p.
7. Branger H., Manna M., Luneau C., et. al. Growth of surface wind-waves in water of finite depth: A laboratory experiment. Coastal Engineering. 2022;177:104174. doi:10.1016/j.coastaleng.2013.02.008
8. Zakharov V.E. Weakly nonlinear waves on the surface of an ideal finite depth fluid. American Mathematical Society Transactions. 1998;182(2):167‒197.
9. Zakharov V. Statistical theory of gravity and capillary waves on the surface of a finite-depth fluid. European Journal of Mechanics. 1999;18(3):327‒344. doi:10.1016/S0997-7546(99)80031-4
10. Montalvo P., Dorignac J., Manna M., et.al. Growth of surface wind-waves in water of finite depth. A theoretical approach. Coastal Engineering. 2013;77:49–56. doi:10.1016/j.coastaleng.2013.02.008
11. Montalvo P., Kraenkel R., Manna M., et.al. Wind-wave amplification mechanisms: Possible models for steep wave events in finite depth. Natural Hazards and Earth System Sciences. 2013;13(11):2805–2813. doi:10.5194/nhess-13-2805-2013
12. Nandi K., Sarka, B., Hossain S., et.al. Wave interaction with multiple thin flexible porous barriers in water of uniform finite depth. Ocean Engineering. 2024;309:118475. doi:10.1016/j.oceaneng.2024.118475
13. Liu S., Waseda T., Zhang X. Four-wave resonant interaction of surface gravity waves in finite water depth. Physical Review Fluids. 2022;7(11). doi:10.1103/PhysRevFluids.7.114803
14. Williams N.J., Peng H. Nonlinear wave modeling over variable depth using extended boussinesq equations. Proceedings of the International Offshore and Polar Engineering Conference. 2012;643–650.
15. Xu Y., Yu X. Enhanced atmospheric wave boundary layer model for evaluation of wind stress over waters of finite depth. Progress in Oceanography. 2021;198:102664. doi:10.1016/j.pocean.2021.102664
16. Ducrozet G., Gouin M. Influence of varying bathymetry in rogue wave occurrence within unidirectional and directional sea-states. Journal of Ocean Engineering and Marine Energy. 2017;3(6):309–324. doi:10.1007/s40722-017-0086-6
17. Peregrine D.H. Long waves on a beach.Journal of Fluid Mechanics. 1967;27(4):815‒827. doi:10.1017/S0022112067002605
18. Gao J., Ma X., Zang Y., et al. Numerical investigation of harbor oscillations induced by focused transient wave groups. Coastal Engineering. 2020;158. doi:10.1016/j.coastaleng.2020.103670
19. Gao J., Ma X., Chen H., et al. On hydrodynamic characteristics of transient harbor resonance excited by double solitary waves. Ocean Engineering. 2021;219. doi:10.1016/j.oceaneng.2020.108345
20. Buccino M., Tuozzo S., Ciccaglione M., et al. Predicting crenulate bay profiles from wave fronts: numerical experiments and empirical formulae. Geosciences. 2021;11(5):208. doi:10.3390/geosciences11050208
21. Berkhoff J.C. Computation of combined refraction-diffraction. Proceedings of 13th Conference on Coastal Engineering. 1972;55–69.
22. Ruban V.P. Water waves over a strongly undulating bottom. Physical Review E. 2004;70(6):066302. doi:10.1103/PhysRevE.70.066302
23. Ruban V.P. Water waves over a time-dependent bottom: Exact description for 2D potential flows. Physics Letters A. 2005;340(1–4):194–200. doi:10.1016/j.physleta.2005.03.07
24. Chalikov D. Numerical modeling of sea waves. Springer. 2016, 330 p. doi:10.1007/978-3-319-32916-1
25. Chalikov D.V. Different approaches to numerical modeling of sea waves. Fundamental and Applied Hydrophysics. 2022;15(1):19–32. doi:10.59887/fpg/u1df-m1x7-1bxg
26. Babanin A.V., Chalikov D., Young I.R., et al. Numerical and laboratory investigation of breaking of steep two-dimensional waves in deep water. Journal of Fluid Mechanics. 2010;644:433–463. doi:10.1017/S002211200999245X
27. Slunyaev A.V., Kokorina A.V. Numerical simulation of the sea rogue waves within the framework of the potential Euler equations. Izvestiya, Atmospheric and Oceanic Physics. 2020;56(2):179–190. doi: 10.1134/S0001433820020127
28. Thomas L.H. Elliptic problems in linear differential equations over a network. Watson Scientific Computing Laboratory Report: Columbia University (New York); 1949.
29. Miles J.W. On the generation of surface waves by shear flows. Journal of Fluid Mechanics. 1957;3(2):185–204. doi:10.1017/S0022112057000567
30. Chalikov D., Rainchik S. Coupled numerical modelling of wind and waves and the theory of the wave boundary layer. BoundaryLayer Meteorology. 2011;138Э:1–41. doi:10.1007/s10546-010-9543-7
31. Hasselmann K., Barnett T.P., Bouws E., et al. Measurements of wind-wave growth and decay during the Joint North Sea Wave Project (JONSWAP). Ergänzungsheft zur Deutschen Hydrographischen Zeitschrift. 1973; A8(12):1–95.
32. Chalikov D. Accelerated reproduction of 2-D periodic waves. Ocean Dynamics. 2021;71(4):309322. doi:10.1007/s10236-021-01450-3
Review
For citations:
Fokina K.V. Three-dimensional phase-resolving surface wave model for finite depth. Fundamental and Applied Hydrophysics. 2025;18(1):19-30. (In Russ.) https://doi.org/10.59887/2073-6673.2025.18(1)-2
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