Russian Journal of Earth Sciences Russian Journal of Earth Sciences Russian Journal of Earth Sciences 1681-1208 69896 10.2205/2024ES000878 snfmci ОРИГИНАЛЬНЫЕ СТАТЬИ ORIGINAL ARTICLES ОРИГИНАЛЬНЫЕ СТАТЬИ Numerical Study on Statistical Characteristics of Developing Waves Численное исследование статистических характеристик развивающегося волнения https://orcid.org/0000-0003-1826-0452 Фокина Карина Владимировна Fokina Karina Vladimirovna fokinakarina@yandex.ru https://orcid.org/0000-0001-8698-9558 Чаликов Дмитрий Викторович Chalikov Dmitriy Viktorovich Институт океанологии им. П.П. Ширшова РАН P.P.Shirshov Institute of Oceanology of the Russian Academy of Science Российский Государственный Гидрометеорологический Университет Санкт-Петербург Россия Russian State Hydrometeorological University Санкт-Петербург Russian Federation Университет Мельбурна Австралия University of Melbourne Australia 14 06 2024 14 06 2024 24 2 1 17 05 09 2023 10 11 2023 https://rjes.ru/en/nauka/article/69896/view

Проведены долгопериодные расчёты эволюции трёхмерных волн, начиная от ранней стадии и заканчивая стабилизацией энергии, на основе фазо-разрешающей двухмерной модели. Анализируется эволюция основных интегральных характеристик и спектральных характеристик, а также распределение вероятности для поля возвышения и вертикальной скорости. На примере первых четырёх статистических моментов для нормированных полей возвышения и поверхностной вертикальной скорости показано, что волновое поле, по-видимому, обладает свойством автомодельности, т. е. независимостью статистической структуры поля от степени развития волн. Этот вывод подтверждён расчётами с трёхмерной моделью

Long-term calculations of the evolution of three-dimensional waves ranging from the early stage to energy stabilization were made on the basis of a two-dimensional phase-resolving model. The evolution of the main integral and spectral characteristics is analyzed along with the probability distribution for the elevation field and vertical velocity. The apparent property of self-similarity (i.e. the independence of the statistical structure of the field from the degree of wave development) for the wave field on the example of the first four moments for normalized fields of elevation and surface vertical velocity is shown. The conclusion is confirmed by the calculations with a three-dimensional model.

 фазо-разрешающее моделирование волновой спектр ветровые волны приток энергии диссипация волновой энергии статистические характеристики волн phase-resolving modeling wave spectrum wind waves energy input dissipation of wave energy statistical characteristics of waves Исследование было выполнено в рамках государственного задания по теме №FMWE-2024-0028. The study was carried out within the framework of the state assignment on topic No. FMWE-2024-0028.

Babanin A. Breaking and Dissipation of Ocean Surface Waves. — Cambridge University Press, 2011. — DOI: 10.1017/CBO9780511736162. Babanin A. Breaking and Dissipation of Ocean Surface Waves. — Cambridge University Press, 2011. — DOI: 10.1017/CBO9780511736162. Causon D. M., Mingham C. G., Qian L. Developments in multi-fluid finite volume free surface capturing methods // Advances in Numerical Simulation of Nonlinear Water Waves. — WORLD SCIENTIFIC, 2010. — С. 397—427. — DOI: 10.1142/9789812836502_0011. Causon D. M., Mingham C. G., Qian L. Developments in multi-fluid finite volume free surface capturing methods // Advances in Numerical Simulation of Nonlinear Water Waves. — WORLD SCIENTIFIC, 2010. — P. 397–427. — DOI: 10.1142/9789812836502_0011. Chalikov D. Correction to: Accelerated reproduction of 2-D periodic waves // Ocean Dynamics. — 2021a. — Т. 71, № 4. — С. 491—491. — DOI: 10.1007/s10236-021-01450-3 Chalikov D. Correction to: Accelerated reproduction of 2-D periodic waves // Ocean Dynamics. — 2021a. — Vol. 71, no. 4. — P. 491–491. — DOI: 10.1007/s10236-021-01450-3. Chalikov D. High-Resolution Numerical Simulation of Surface Wave Development under the Action of Wind // Geophysics and Ocean Waves Studies. — IntechOpen, 2021b. — DOI: 10.5772/intechopen.92262. Chalikov D. High-Resolution Numerical Simulation of Surface Wave Development under the Action of Wind // Geophysics and Ocean Waves Studies. — IntechOpen, 2021b. — DOI: 10.5772/intechopen.92262. Chalikov D. V. Numerical Modeling of Sea Waves. — Springer International Publishing, 2016. — DOI: 10.1007/978-3-319- 32916-1. Chalikov D. V. Numerical Modeling of Sea Waves. — Springer International Publishing, 2016. — DOI: 10.1007/978-3-319- 32916-1. Ducrozet G., Bonnefoy F., Le Touz´e D. и др. 3-D HOS simulations of extreme waves in open seas // Natural Hazards and Earth System Sciences. — 2007. — Т. 7, № 1. — С. 109—122. — DOI: 10.5194/nhess-7-109-2007. Ducrozet G., Bonnefoy F., Le Touzé D., et al. 3-D HOS simulations of extreme waves in open seas // Natural Hazards and Earth System Sciences. — 2007. — Vol. 7, no. 1. — P. 109–122. — DOI: 10.5194/nhess-7-109-2007. Ducrozet G., Bonnefoy F., Le Touz´e D. и др. HOS-ocean: Open-source solver for nonlinear waves in open ocean based on High-Order Spectral method // Computer Physics Communications. — 2016. — Т. 203. — С. 245—254. — DOI: 10.1016/j.cpc.2016.02.017. Ducrozet G., Bonnefoy F., Le Touzé D., et al. HOS-ocean: Open-source solver for nonlinear waves in open ocean based on High-Order Spectral method // Computer Physics Communications. — 2016. — Vol. 203. — P. 245–254. — DOI: 10.1016/j.cpc.2016.02.017. Engsig-Karup A. P., Bingham H. B., Lindberg O. An efficient flexible-order model for 3D nonlinear water waves // Journal of Computational Physics. — 2009. — Т. 228, № 6. — С. 2100—2118. — DOI: 10.1016/j.jcp.2008.11.028. Engsig-Karup A. P., Bingham H. B., Lindberg O. An efficient flexible-order model for 3D nonlinear water waves // Journal of Computational Physics. — 2009. — Vol. 228, no. 6. — P. 2100–2118. — DOI: 10.1016/j.jcp.2008.11.028. Engsig-Karup A. P., Madsen M. G., Glimberg S. L. A massively parallel GPU-accelerated model for analysis of fully nonlinear free surface waves // International Journal for Numerical Methods in Fluids. — 2011. — Т. 70, № 1. — С. 20—36. — DOI: 10.1002/fld.2675. Engsig-Karup A. P., Madsen M. G., Glimberg S. L. A massively parallel GPU-accelerated model for analysis of fully nonlinear free surface waves // International Journal for Numerical Methods in Fluids. — 2011. — Vol. 70, no. 1. — P. 20–36. — DOI: 10.1002/fld.2675. Fructus D., Clamond D., Grue J. и др. An efficient model for three-dimensional surface wave simulations // Journal of Computational Physics. — 2005. — Т. 205, № 2. — С. 665—685. — DOI: 10.1016/j.jcp.2004.11.027. Fructus D., Clamond D., Grue J., et al. An efficient model for three-dimensional surface wave simulations // Journal of Computational Physics. — 2005. — Vol. 205, no. 2. — P. 665–685. — DOI: 10.1016/j.jcp.2004.11.027. Greaves D. Advances in Numerical Simulation of Nonlinear Water Waves // Advances in Numerical Simulation of Nonlinear Water Waves. — WORLD SCIENTIFIC, 2010. — С. 357—396. — DOI: 10.1142/9789812836502_0010. Greaves D. Advances in Numerical Simulation of Nonlinear Water Waves // Advances in Numerical Simulation of Nonlinear Water Waves. — WORLD SCIENTIFIC, 2010. — P. 357–396. — DOI: 10.1142/9789812836502_0010. Issa R., Violeau D., Lee E.-S. и др. Modelling nonlinear water waves with RANS and LES SPH models // Advances in Numerical Simulation of Nonlinear Water Waves. — WORLD SCIENTIFIC, 2010. — С. 497—537. — DOI: 10.1142/9789812836502_0014. Issa R., Violeau D., Lee E.-S., et al. Modelling nonlinear water waves with RANS and LES SPH models // Advances in Numerical Simulation of Nonlinear Water Waves. — WORLD SCIENTIFIC, 2010. — P. 497–537. — DOI: 10.1142/9789812836502_0014. Kim K. S., Kim M. H., Park J.-C. Development of Moving Particle Simulation Method for Multiliquid-Layer Sloshing // Mathematical Problems in Engineering. — 2014. — Т. 2014. — С. 1—13. — DOI: 10.1155/2014/350165. Kim K. S., Kim M. H., Park J.-C. Development of Moving Particle Simulation Method for Multiliquid-Layer Sloshing // Mathematical Problems in Engineering. — 2014. — Vol. 2014. — P. 1–13. — DOI: 10.1155/2014/350165. Kim Y. J., Baek H. M., Yang Y. J. и др. A Study on the High-Order Spectral Model Capability to Simulate a Fully Developed Nonlinear Sea States // Journal of Ocean Engineering and Technology. — 2023. — Т. 37, № 1. — С. 20—30. —DOI: 10.26748/KSOE.2022.034. Kim Y. J., Baek H. M., Yang Y. J., et al. A Study on the High-Order Spectral Model Capability to Simulate a Fully Developed Nonlinear Sea States // Journal of Ocean Engineering and Technology. — 2023. — Vol. 37, no. 1. — P. 20–30. — DOI: 10.26748/KSOE.2022.034. Lubin P., Caltagirone J.-P. Large eddy simulation of the hydrodynamics generated by breaking waves // Advances in Numerical Simulation of Nonlinear Water Waves. — WORLD SCIENTIFIC, 2010. — С. 575—604. — DOI: 10.1142/9789812836502_0016. Lubin P., Caltagirone J.-P. Large eddy simulation of the hydrodynamics generated by breaking waves // Advances in Numerical Simulation of Nonlinear Water Waves. — WORLD SCIENTIFIC, 2010. — P. 575–604. — DOI: 10.1142/9789812836502_0016. Ma Q. W., Yan S. Qale-FEM method and its application to the simulation of free responses of floating bodies and overturning waves // Advances in Numerical Simulation of Nonlinear Water Waves. — WORLD SCIENTIFIC, 2010. — С. 165—202. — DOI: 10.1142/9789812836502_0005. Ma Q. W., Yan S. Qale-FEM method and its application to the simulation of free responses of floating bodies and overturning waves // Advances in Numerical Simulation of Nonlinear Water Waves. — WORLD SCIENTIFIC, 2010. — P. 165–202. — DOI: 10.1142/9789812836502_0005. Miles J. W. On the generation of surface waves by shear flows // Journal of Fluid Mechanics. — 1957. — Т. 3, № 02. — С. 185. — DOI: 10.1017/S0022112057000567. Miles J. W. On the generation of surface waves by shear flows // Journal of Fluid Mechanics. — 1957. — Vol. 3, no. 02. — P. 185. — DOI: 10.1017/S0022112057000567. Thomas L. H. Elliptic problems in linear differential equations over a network. — Columbia University (New York) : Watson Scientific Computing Laboratory Report, 1949. Thomas L. H. Elliptic problems in linear differential equations over a network. — Columbia University (New York) : Watson Scientific Computing Laboratory Report, 1949. Tolman H. L. User Manual and System Documentation of WAVEWATCH-III Version 3.14. — NOAA/NWS/NCEP/MMAB, 2009. — 220 с. Tolman H. L. User Manual and System Documentation of WAVEWATCH-III Version 3.14. — NOAA/NWS/NCEP/MMAB, 2009. — 220 p. Young D.-L., Wu N.-J., Tsay T.-K. Method of fundamental solutions for fully nonlinear water waves // Advances in Numerical Simulation of Nonlinear Water Waves. — WORLD SCIENTIFIC, 2010. — С. 325—355. — DOI: 10.1142/9789812836502_0009. Young D.-L., Wu N.-J., Tsay T.-K. Method of fundamental solutions for fully nonlinear water waves // Advances in Numerical Simulation of Nonlinear Water Waves. — WORLD SCIENTIFIC, 2010. — P. 325–355. — DOI: 10.1142/9789812836502_0009.