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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">hydrophysics</journal-id><journal-title-group><journal-title xml:lang="ru">Фундаментальная и прикладная гидрофизика</journal-title><trans-title-group xml:lang="en"><trans-title>Fundamental and Applied Hydrophysics</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2073-6673</issn><issn pub-type="epub">2782-5221</issn><publisher><publisher-name>St. Petersburg Research Center of the Russian Academy of Sciences</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.59887/2073-6673.2025.19(1)-3</article-id><article-id custom-type="edn" pub-id-type="custom">kluskm</article-id><article-id custom-type="elpub" pub-id-type="custom">hydrophysics-1516</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ФУНДАМЕНТАЛЬНЫЕ ВОПРОСЫ ГИДРОФИЗИКИ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>FUNDAMENTAL ISSUES OF HYDROPHYSICS</subject></subj-group></article-categories><title-group><article-title>Численное моделирование ветровых волн с учетом притока энергии и диссипации</article-title><trans-title-group xml:lang="en"><trans-title>Numerical modeling of wind waves with energy input and dissipation</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-8698-9558</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Чаликов</surname><given-names>Д. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Chalikov</surname><given-names>D. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>ЧАЛИКОВ Дмитрий Викторович, доктор физико-математических наук, профессор, ведущий научный сотрудник</p><p>117997, Москва, Нахимовский проспект, д. 36</p><p>3010 Виктория, Австралия</p></bio><bio xml:lang="en"><p>D. V. Chalikov</p><p>36 Nakhimovsky Prosp., Moscow, 117997</p><p>Victoria 3010, Australia</p></bio><email xlink:type="simple">dmitry-chalikov@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-1826-0452</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Фокина</surname><given-names>К. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Fokina</surname><given-names>K. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>ФОКИНА Карина Владимировна, кандидат физико-математических наук, младший научный сотрудник</p><p>117997, Москва, Нахимовский проспект, д. 36</p></bio><bio xml:lang="en"><p>K. V. Fokina</p><p>36 Nakhimovsky Prosp., Moscow, 117997</p></bio><email xlink:type="simple">fokinakarina@yandex.ru</email><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Институт океанологии им. П.П. Ширшова РАН; Университет Мельбурна</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Shirshov Institute of Oceanology, Russian Academy of Sciences; University of Melbourne</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Институт океанологии им. П.П. Ширшова РАН</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Shirshov Institute of Oceanology, Russian Academy of Sciences</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2026</year></pub-date><pub-date pub-type="epub"><day>30</day><month>03</month><year>2026</year></pub-date><volume>19</volume><issue>1</issue><fpage>45</fpage><lpage>58</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Чаликов Д.В., Фокина К.В., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Чаликов Д.В., Фокина К.В.</copyright-holder><copyright-holder xml:lang="en">Chalikov D.V., Fokina K.V.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://hydrophysics.spbrc.ru/jour/article/view/1516">https://hydrophysics.spbrc.ru/jour/article/view/1516</self-uri><abstract><p>В статье рассматривается актуальная проблема в области моделирования ветровых волн, связанная с необходимостью точного описания притока энергии от ветра и диссипации волновой энергии. Отмечается, что корректный учет этих процессов является важным шагом для повышения точности волновых прогнозов и оценки рисков, возникающих при экстремальных волновых явлениях. В статье представлены примеры параметризации притока и диссипации энергии, включенные в фазо-разрешающую модель трехмерных волн TriDWave, основанную на нелинейных уравнениях Эйлера. Приток энергии рассчитывается на основе модифицированной теории Майлза, а диссипация — с помощью оператора, активируемого в зонах, близких к обрушению, и осуществляющего быстрое сглаживание поверхности. На основе длительных численных экспериментов показано, что включение этих параметризаций позволяет реалистично моделировать развитие волнового поля: воспроизводить рост полной энергии, смещение спектрального пика в сторону меньших волновых чисел, а также формирование волн с характерной вертикальной и горизонтальной асимметрией. Представленный подход закладывает основу для разработки более совершенных параметризаций физических процессов в фазо-разрешающих волновых моделях и способствует созданию надежных систем прогноза ветрового волнения.</p></abstract><trans-abstract xml:lang="en"><p>The paper addresses a critical challenge in wind wave modeling — the need for accurate representation of energy input from wind and wave energy dissipation. It is emphasized that reliable incorporation of these processes is essential for improving the accuracy of operational wave forecasting models and for assessing risks associated with extreme wave events. The study introduces specific parameterizations for energy input and dissipation, implemented within the three-dimensional potential wave model TriDWave, which is based on nonlinear Euler equations in a periodic domain. Energy input is computed using a modified Miles theory, while dissipation is modeled via an operator triggered in near-breaking wave regions, facilitating rapid surface smoothing. Long-term numerical simulations demonstrate that incorporating these parameterizations enables realistic modeling of wave field evolution under steady wind forcing, including the reproduction of total energy growth, spectral peak downshift, and the formation of waves with characteristic vertical and horizontal asymmetry. The presented approach establishes a foundation for developing more refined physical parameterizations in wave models and contributes to the creation of reliable wind wave forecasting systems.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>потенциальные поверхностные волны</kwd><kwd>численное моделирование</kwd><kwd>приток энергии</kwd><kwd>диссипация волн</kwd><kwd>спектр волн</kwd><kwd>метод преобразования Фурье</kwd><kwd>статистические характеристики волн</kwd><kwd>экстремальные волны</kwd></kwd-group><kwd-group xml:lang="en"><kwd>potential surface waves</kwd><kwd>numerical modeling</kwd><kwd>energy input</kwd><kwd>wave dissipation</kwd><kwd>wave spectrum</kwd><kwd>Fourier transform method</kwd><kwd>statistical wave characteristics</kwd><kwd>extreme waves</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Работа выполнена в рамках государственного задания Минобрнауки России для ИОРАН (тема № FMWE‑2024-0028).</funding-statement><funding-statement xml:lang="en">The research was carried out within the state assignment of Ministry of Science and Higher Education of the Russian Federation for IO RAS (theme № FMWE‑2024-0028).</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Chalikov D. 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