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  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher-id">Physical Oceanography</journal-id>
      <journal-title-group>
        <journal-title xml:lang="en">Physical Oceanography</journal-title>
      </journal-title-group>
      <issn publication-format="print">1573-160X</issn>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="publisher-id">20230606</article-id>
      
      <article-categories>
        <subj-group subj-group-type="toc-heading" xml:lang="en">
          <subject>Experimental and field research</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">Field Investigations of the Geometric Features of Wind Wave Breaking</article-title>
      </title-group>

      <contrib-group>
        <contrib contrib-type="author">
          <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-7452-8703</contrib-id>
          <contrib-id contrib-id-type="scopus">23492523000</contrib-id>
          <contrib-id contrib-id-type="spin">7288-8023</contrib-id>
          <name>
            <surname>Korinenko</surname>
            <given-names>A. E.</given-names>
          </name>
          <address>
            <country country="RU">Russian Federation</country>
          </address>
          <email>korinenko.alex@mhi-ras.ru</email>
          <xref ref-type="aff" rid="aff1"/>
        </contrib>
        <contrib contrib-type="author">
          <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-5799-454X</contrib-id>
          <contrib-id contrib-id-type="researcherid">F-8709-2014</contrib-id>
          <contrib-id contrib-id-type="scopus">23012976200</contrib-id>
          <contrib-id contrib-id-type="spin">9206-3020</contrib-id>
          <name>
            <surname>Malinovsky</surname>
            <given-names>V. V.</given-names>
          </name>
          <address>
            <country country="RU">Russian Federation</country>
          </address>
          <email>vladimir.malinovsky@mhi-ras.ru</email>
          <xref ref-type="aff" rid="aff1"/>
        </contrib>
      </contrib-group>

      <aff id="aff1">
        <institution>Marine Hydrophysical Institute of RAS</institution>
        <addr-line>Sevastopol</addr-line>
        <country country="RU">Russian Federation</country>
      </aff>

      <pub-date date-type="pub" iso-8601-date="2023-12-31" publication-format="electronic">
        <day>31</day>
        <month>12</month>
        <year>2023</year>
      </pub-date>
      <volume>30</volume>
      <issue>6</issue>
      <fpage>776</fpage>
      <lpage>791</lpage>

      <history>
        <date date-type="received" iso-8601-date="2023-04-26">
          <day>26</day>
          <month>04</month>
          <year>2023</year>
        </date>
        <date date-type="rev-recd" iso-8601-date="2023-08-28">
          <day>28</day>
          <month>08</month>
          <year>2023</year>
        </date>
        <date date-type="accepted" iso-8601-date="2023-09-06">
          <day>06</day>
          <month>09</month>
          <year>2023</year>
        </date>
      </history>

      <permissions>
        <copyright-statement xml:lang="en">Copyright ©; 2023, A. E. Korinenko, V. V. Malinovsky</copyright-statement>
        <copyright-year>2023</copyright-year>
        <copyright-holder xml:lang="en">A. E. Korinenko, V. V. Malinovsky</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://physical-oceanography.ru/repository/issues/2023/06/06/" xlink:title="Article page">https://physical-oceanography.ru/repository/issues/2023/06/06/</self-uri>
      
      <abstract xml:lang="en">
        <p><bold>Purpose.</bold> The paper is purposed at studying temporal variability of the geometric dimensions of wind wave breaking under natural conditions and at assessing the fraction of the sea surface covered with foam using the distribution of the breaking wave crest lengths.</p>
        <p><bold>Methods and Results.</bold> Field studies of the wave breaking characteristics were carried out from the stationary oceanographic platform located at 500 m off the Katsiveli coast (Black Sea hydrophysical subsatellite polygon). Geometric dimensions of wave breaking in the active phase and the velocity of wave movement were determined using video records of sea surface. Processing of video frame sequences has resulted in formation of the array of crest lengths, and the array of widths and areas of the varying in time foam structures. Meteorological information was obtained simultaneously with video records.</p>
        <p><bold>Conclusions.</bold> A connection independent of wind and wave conditions was established experimentally between the wave breaking geometric dimensions and the breaking wave length: the average width of breaking is proportional to the length of a breaking wave, the average area – to the squared length of a carrier wave. The values of these ratios are 0.03 and 0.002, respectively, that confirms the geometric similarity of wave breaking. It is shown that the length and width of an individual wave breaking increase at a constant rate, the value of which is conditioned by the scale of a breaking wave. The geometric characteristics of wave breaking normalized to the length of a breaking wave are linearly dependent on dimensionless time and independent of the scales and velocities of breaking waves. To calculate the fraction of sea surface covered with foam, the distributions of the wave breaking lengths were used. The field data values are shown to be adequately corresponding to the calculations by the model proposed by O. M. Phillips.</p>
      </abstract>

      <kwd-group>
        <kwd>wind wave breaking</kwd>
        <kwd>field studies</kwd>
        <kwd>distribution of breaking lengths</kwd>
        <kwd>breaking similarity</kwd>
        <kwd>fraction of the sea surface covered with wave breaking foam</kwd>
        <kwd>growth rate of linear dimensions of breaking</kwd>
      </kwd-group>

      <funding-group>
        <funding-statement xml:lang="en">The study was financially supported by the Russian Science Foundation grant No. 21-17-00236, https://rscf.ru/project/21-17-00236/. The study involved the archival data obtained within the framework of the theme of state assignment FNNN-2021-0004 "Fundamental research of oceanological processes that determine state and evolution of the marine environment under the influence of natural and anthropogenic factors, based on observation and modeling methods".</funding-statement>
      </funding-group>
    </article-meta>
  </front>

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