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  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher-id">Morskoj gidrofizičeskij žurnal</journal-id>
      <journal-title-group>
        <journal-title xml:lang="en">Morskoj gidrofizičeskij žurnal</journal-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Морской гидрофизический журнал</trans-title>
        </trans-title-group>
      </journal-title-group>
      <issn publication-format="print">0233-7584</issn>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="publisher-id">20250106</article-id>
      <article-id pub-id-type="edn">JZPQGE</article-id>
      
      <article-categories>
        <subj-group subj-group-type="toc-heading" xml:lang="en">
          <subject>Mathematical modeling of marine systems</subject>
        </subj-group>
        <subj-group subj-group-type="toc-heading" xml:lang="ru">
          <subject>Математическое моделирование морских систем</subject>
        </subj-group>
        <subj-group subj-group-type="article-type">
          <subject>Research Article</subject>
        </subj-group>
      </article-categories>

      <title-group>
        <article-title xml:lang="en">Non-Stationary Turbulence Model for the Upper Boundary Layer of the Sea</article-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Нестационарная модель турбулентности для верхнего пограничного слоя моря</trans-title>
        </trans-title-group>
      </title-group>

      <contrib-group>
        <contrib contrib-type="author">
          <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-1078-6425</contrib-id>
          <contrib-id contrib-id-type="researcherid">G-3180-2013</contrib-id>
          <contrib-id contrib-id-type="spin">1078-6425</contrib-id>
          <name-alternatives>
            <name xml:lang="en">
              <surname>Chukharev</surname>
              <given-names>A. M.</given-names>
            </name>
            <name xml:lang="ru">
              <surname>Чухарев</surname>
              <given-names>А. М.</given-names>
            </name>
          </name-alternatives>
          <address>
            <country country="RU">Russian Federation</country>
          </address>
          <bio xml:lang="ru"><p>главный научный сотрудник, отдел турбулентности, ФГБУН ФИЦ МГИ (299011, Россия, г. Севастополь, ул. Капитанская, д. 2), доктор физико-математических наук</p></bio>
          <email>alexchukh@mail.ru</email>
          <xref ref-type="aff" rid="aff1"/>
        </contrib>
      </contrib-group>

      <aff-alternatives id="aff1">
        <aff xml:lang="en">
          <institution>Marine Hydrophysical Institute, Russian Academy of Sciences</institution>
          <addr-line>Sevastopol</addr-line>
          <country>Russia</country>
        </aff>
        <aff xml:lang="ru">
          <institution>Морской гидрофизический институт РАН</institution>
          <addr-line>Севастополь</addr-line>
          <country>Россия</country>
        </aff>
      </aff-alternatives>

      <pub-date date-type="pub" iso-8601-date="2025-02-28" publication-format="electronic">
        <day>28</day>
        <month>02</month>
        <year>2025</year>
      </pub-date>
      <volume>41</volume>
      <issue>1</issue>
      <fpage>83</fpage>
      <lpage>100</lpage>

      <history>
        <date date-type="received" iso-8601-date="2024-09-03">
          <day>03</day>
          <month>09</month>
          <year>2024</year>
        </date>
        <date date-type="rev-recd" iso-8601-date="2024-10-10">
          <day>10</day>
          <month>10</month>
          <year>2024</year>
        </date>
        <date date-type="accepted" iso-8601-date="2024-11-20">
          <day>20</day>
          <month>11</month>
          <year>2024</year>
        </date>
      </history>

      <permissions>
        <copyright-statement xml:lang="en">Copyright ©; 2025, Chukharev A.M.</copyright-statement>
        <copyright-statement xml:lang="ru">Copyright ©; 2025, Чухарев А. М.</copyright-statement>
        <copyright-year>2025</copyright-year>
        <copyright-holder xml:lang="en">Chukharev A.M.</copyright-holder>
        <copyright-holder xml:lang="ru">Чухарев А. М.</copyright-holder>
        <ali:free_to_read xmlns:ali="http://www.niso.org/schemas/ali/1.0/"/>
        <license>
          <ali:license_ref xmlns:ali="http://www.niso.org/schemas/ali/1.0/">https://creativecommons.org/licenses/by-nc/4.0/</ali:license_ref>
        </license>
      </permissions>
      <self-uri xlink:href="https://xn--c1agq7a.xn--p1ai/repository/issues/2025/01/06/" xlink:title="Страница статьи">https://xn--c1agq7a.xn--p1ai/repository/issues/2025/01/06/</self-uri>
      
      <abstract xml:lang="en">
        <p><bold>Purpose</bold>. The purpose of the study is to develop the physical concepts of dynamic interaction of two media on small and submesoscales, as well as to create an objective model for describing the turbulent regime of the sea near-surface layer.</p>
        <p><bold>Methods and Results</bold>. Significant scales of turbulence energy supply are established, and a non-stationary numerical model of turbulent exchange in the near-surface layer of the sea is proposed based on the large arrays of experimental data on marine turbulence intensity under different hydrometeorological conditions. Four basic generation mechanisms are considered as the sources of turbulence, namely drift current velocity shear, surface waves and their breakings, and submesoscale eddy structures. The influence of the latter is assessed through the structural function calculated using the synchronous measurements of current velocity in two points. The numerical solutions for velocity profiles, turbulence energy, and dissipation rate are compared to the experimental data, at that the necessary model constants are selected. Verification of the calculations has shown their good agreement with the measurements in a fairly wide range of wind speeds including the weak winds for which the other models yield the significantly lower results as compared to the experimental data.</p>
        <p><bold>Conclusions</bold>. A non-stationary model is proposed for calculating the turbulence characteristics in the upper mixed layer of the sea. The application of structural function in the turbulent energy balance equation improves the agreement between model calculations and experimental data. The developed model quite reliably describes the turbulent structure of the layer under study and permits to calculate the intensity of vertical turbulent exchange in different hydrometeorological conditions.</p>
      </abstract>
      
      <trans-abstract xml:lang="ru">
        <p><bold>Цель</bold>. Развитие физических представлений о динамическом взаимодействии двух сред на малых и субмезомасштабах и создание объективной модели для описания турбулентного режима приповерхностного слоя моря – цель статьи.</p>
        <p><bold>Методы и результаты.</bold> На основе больших массивов экспериментальных данных об интенсивности морской турбулентности при различных гидрометеорологических условиях установлены значимые масштабы энергоснабжения турбулентности и предложена нестационарная численная модель турбулентного обмена в приповерхностном слое моря. В качестве источников турбулентности рассмотрены четыре основных механизма генерации: сдвиг скорости дрейфового течения, поверхностные волны и их обрушения, субмезомасштабные вихревые структуры. Влияние последних оценивается через структурную функцию, рассчитанную по синхронным измерениям скорости течения в двух точках. Численные решения для профилей скорости, энергии турбулентности и скорости диссипации сопоставлялись с экспериментальными данными, при этом подобраны необходимые модельные константы. Верификация результатов расчетов показала их хорошее соответствие данным измерений в достаточно широком диапазоне скоростей ветра, в том числе и при слабых ветрах, когда другие модели дают сильно заниженный результат по сравнению с экспериментом.</p>
        <p><bold>Выводы.</bold> Предложена нестационарная модель для расчета характеристик турбулентности в верхнем перемешанном слое моря. Использование структурной функции в уравнении баланса турбулентной энергии улучшает соответствие модельных расчетов и экспериментальных данных. Разработанная модель достоверно описывает турбулентную структуру исследуемого слоя и позволяет рассчитывать интенсивность вертикального турбулентного обмена в различных гидрометеорологических условиях.</p>
      </trans-abstract>

      <kwd-group xml:lang="en">
        <kwd>sea turbulence</kwd>
        <kwd>near-surface layer</kwd>
        <kwd>turbulence generation mechanisms</kwd>
        <kwd>structural function</kwd>
        <kwd>non-stationary model of turbulence</kwd>
        <kwd>dissipation rate</kwd>
        <kwd>experimental data</kwd>
      </kwd-group>
      <kwd-group xml:lang="ru">
        <kwd>морская турбулентность</kwd>
        <kwd>приповерхностный слой</kwd>
        <kwd>механизмы генерации турбулентности</kwd>
        <kwd>структурная функция</kwd>
        <kwd>нестационарная модель турбулентности</kwd>
        <kwd>скорость диссипации</kwd>
        <kwd>экспериментальные данные</kwd>
      </kwd-group>

      <funding-group>
        <funding-statement xml:lang="en">Experimental studies and data preprocessing were carried out within the framework of theme of state assignment of FSBSI FRC MHI FNNN-2021-0004 "Oceanological processes". Data analysis and model development and verification were performed with financial support of RSF grant 22-17-00150.</funding-statement>
        <funding-statement xml:lang="ru">в рамках темы госзадания ФГБУН ФИЦ МГИ FNNN-2021-0004 «Океанологические процессы» выполнены экспериментальные исследования и предварительная обработка данных. При финансовой поддержке гранта РНФ 22-17-00150 выполнены анализ данных, разработка и верификация модели.</funding-statement>
      </funding-group>
    </article-meta>
  </front>

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