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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">vmait</journal-id><journal-title-group><journal-title xml:lang="ru">Computational Mathematics and Information Technologies</journal-title><trans-title-group xml:lang="en"><trans-title>Computational Mathematics and Information Technologies</trans-title></trans-title-group></journal-title-group><issn pub-type="epub">2587-8999</issn><publisher><publisher-name>Донской государственный технический университет</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.23947/2587-8999-2023-6-1-34-40</article-id><article-id custom-type="elpub" pub-id-type="custom">vmait-49</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>Статьи</subject></subj-group></article-categories><title-group><article-title>Моделирование пространственно-трехмерных волновых процессов в мелководных водоемах с учетом особенностей вертикального турбулентного обмена</article-title><trans-title-group xml:lang="en"><trans-title>Original article Spatial-three-dimensional wave processes’ modeling in shallow water bodies taking into account the vertical turbulent exchange features</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-7911-3558</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Проценко</surname><given-names>Е. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Protsenko</surname><given-names>E. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Елена Анатольевна Проценко - кандидат физико-математических наук, доцент кафедры математики, ведущий научный сотрудник.</p><p>347936, Таганрог, ул. Инициативная, 48</p></bio><bio xml:lang="en"><p>48, Initiative St., Taganrog, Rostov region</p></bio><email xlink:type="simple">eapros@rambler.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/0000-0002-9037-5556</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Панасенко</surname><given-names>Н. Д.</given-names></name><name name-style="western" xml:lang="en"><surname>Panasenko</surname><given-names>N. D.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Панасенко Наталья Дмитриевна - научный сотрудник.</p><p>347936, Таганрог, ул. Инициативная, 48</p></bio><bio xml:lang="en"><p>48, Initiative St., Taganrog, Rostov region</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-2449-8531</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Стражко</surname><given-names>А. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Strazhko</surname><given-names>A. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Стражко Александр Валентинович - научный сотрудник.</p><p>347936, Таганрог, ул. Инициативная, 48</p></bio><bio xml:lang="en"><p>48, Initiative St., Taganrog, Rostov region</p></bio><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Таганрогский институт имени А. П. Чехова (филиал) РГЭУ (РИНХ)</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Taganrog Institute named after A.P. Chekhov (branch) of RSUE</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2023</year></pub-date><pub-date pub-type="epub"><day>26</day><month>03</month><year>2023</year></pub-date><volume>7</volume><issue>1</issue><fpage>34</fpage><lpage>40</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Проценко Е.А., Панасенко Н.Д., Стражко А.В., 2023</copyright-statement><copyright-year>2023</copyright-year><copyright-holder xml:lang="ru">Проценко Е.А., Панасенко Н.Д., Стражко А.В.</copyright-holder><copyright-holder xml:lang="en">Protsenko E.A., Panasenko N.D., Strazhko A.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://www.cmit-journal.ru/jour/article/view/49">https://www.cmit-journal.ru/jour/article/view/49</self-uri><abstract><sec><title>Введение</title><p>Введение. Достоверное предсказание показателей турбулентных потоков является весьма сложной задачей, что объясняется исключительной физической сложностью турбулентности, в частности ее вероятностной природой, широким пространственно-временным спектром и принципиально трехмерным нестационарным характером. Несмотря на проведение широкого круга исследований, ориентированных на рассматриваемую проблему, в них не была достаточно полно отражена вся совокупность разнообразных факторов и процессов, влияющих на структуру и параметры вертикального турбулентного перемешивания. Это указывает на необходимость проведения системного анализа проблемы и моделирования подобных сложно формализуемых систем. Целью работы является построение сценария изменения гидродинамических волновых процессов береговой зоны на основе усовершенствованной математической модели волновых процессов.</p></sec><sec><title>Материалы и методы</title><p>Материалы и методы. Исследуются пространственно-трехмерные волновые процессы в мелководных водоемах с учетом особенностей турбулентного обмена в зависимости от источника и локализации в столбе жидкости. Рассматривается влияние регулярных волновых процессов на турбулентный обмен по вертикали с помощью математической модели волновых процессов, базирующейся на системе уравнений Навье-Стокса. Модель включает в себя три уравнения движения в областях с динамически изменяемой геометрией расчетной области. Результаты исследования. На основе разработанного комплекса программ построен сценарий изменения гидродинамических волновых процессов береговой зоны, предсказано формирование вихревых структур. Обсуждение и заключения. Доказано разделение волнового потока на приповерхностный макротурбулентный слой, вызванный волновым движением, и нижерасположенный слой с фоновой гидродинамической турбулентностью, сила и интенсивность турбулентности изменялись синхронно с волновыми колебаниями, демонстрируя явно выраженную асимметрию генерации турбулентности по всей толще воды.</p></sec></abstract><trans-abstract xml:lang="en"><sec><title>Introduction</title><p>Introduction. Reliable prediction of indicators of turbulent flows is a very difficult task, which is explained by the exceptional physical complexity of turbulence, in particular its probabilistic nature, a wide space-time spectrum and a fundamentally three-dimensional non-stationary nature. Despite conducting a wide range of studies focused on the problem under consideration, they did not fully reflect the totality of various factors and processes affecting the structure and parameters of vertical turbulent mixing. This indicates the need for a systematic analysis of the problem and modeling of such complex formalized systems. The aim of the work is to construct a scenario of changes in hydrodynamic wave processes of the coastal zone, based on an improved mathematical model of wave processes.</p></sec><sec><title>Materials and methods</title><p>Materials and methods. The article is devoted to the study of spatial-three-dimensional wave processes in shallow water bodies, taking into account the features of turbulent exchange depending on the source and localization in the column of liquid, as well as the study of the influence of regular wave processes on turbulent exchange and vertically using a mathematical model of wave processes based on the system of Navier-Stokes equations, including three equations of motion in the with dynamically changing geometry of the computational domain.</p></sec><sec><title>The results of the study</title><p>The results of the study. Based on the developed software package, a scenario of changes in hydrodynamic wave processes of the coastal zone is constructed, the formation of vortex structures is predicted. Discussion and conclusions. The separation of the wave flow into a near-surface macroturbulent layer caused by wave motion and a lower layer with background hydrodynamic turbulence is proved, the strength and intensity of turbulence changed synchronously with wave oscillations, demonstrating a pronounced asymmetry of turbulence generation throughout the water column.</p></sec></trans-abstract><kwd-group xml:lang="ru"><kwd>трехмерная модель гидродинамики</kwd><kwd>вертикальный турбулентный обмен</kwd><kwd>численные методы</kwd><kwd>волновые процессы</kwd><kwd>фильтрация данных</kwd></kwd-group><kwd-group xml:lang="en"><kwd>three-dimensional model of hydrodynamics</kwd><kwd>vertical turbulent exchange</kwd><kwd>numerical methods</kwd><kwd>wave processes</kwd><kwd>data filtering</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Исследование выполнено за счет гранта Российского научного фонда № 23-21-00210, https://rscf.ru/project/23-21-00210/»</funding-statement><funding-statement xml:lang="en">The research was carried out at the expense of the grant of the Russian Science Foundation No. 2321-00210, https://rscf.ru/project/23-21-00210/»</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">Ferrer, M. 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