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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>
    <trans-title-group xml:lang="ru">
     <trans-title>Physical Oceanography</trans-title>
    </trans-title-group>
   </journal-title-group>
   <issn publication-format="online">1573-160X</issn>
  </journal-meta>
  <article-meta>
   <article-id pub-id-type="publisher-id">101166</article-id>
   <article-categories>
    <subj-group subj-group-type="toc-heading" xml:lang="ru">
     <subject>ANALYSIS OF OBSERVATIONS AND METHODS OF CALCULATING HYDROPHYSICAL FIELDS IN THE OCEAN</subject>
    </subj-group>
    <subj-group subj-group-type="toc-heading" xml:lang="en">
     <subject>ANALYSIS OF OBSERVATIONS AND METHODS OF CALCULATING HYDROPHYSICAL FIELDS IN THE OCEAN</subject>
    </subj-group>
    <subj-group>
     <subject>ANALYSIS OF OBSERVATIONS AND METHODS OF CALCULATING HYDROPHYSICAL FIELDS IN THE OCEAN</subject>
    </subj-group>
   </article-categories>
   <title-group>
    <article-title xml:lang="en">Estimation of the Stationarity Interval of Wind Wave Field</article-title>
    <trans-title-group xml:lang="ru">
     <trans-title>Estimation of the Stationarity Interval of Wind Wave Field</trans-title>
    </trans-title-group>
   </title-group>
   <contrib-group content-type="authors">
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Saprykina</surname>
       <given-names>Yana </given-names>
      </name>
      <name xml:lang="en">
       <surname>Saprykina</surname>
       <given-names>Yana </given-names>
      </name>
     </name-alternatives>
     <xref ref-type="aff" rid="aff-1"/>
    </contrib>
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Divinsky</surname>
       <given-names>Boris </given-names>
      </name>
      <name xml:lang="en">
       <surname>Divinsky</surname>
       <given-names>Boris </given-names>
      </name>
     </name-alternatives>
     <xref ref-type="aff" rid="aff-2"/>
    </contrib>
    <contrib contrib-type="author">
     <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-0045-0282</contrib-id>
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Stremel</surname>
       <given-names>M. N.</given-names>
      </name>
      <name xml:lang="en">
       <surname>Stremel</surname>
       <given-names>M. N.</given-names>
      </name>
     </name-alternatives>
     <email>shtremel@ocean.ru</email>
     <xref ref-type="aff" rid="aff-3"/>
    </contrib>
    <contrib contrib-type="author">
     <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-7013-339X</contrib-id>
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Likutova</surname>
       <given-names>O. A.</given-names>
      </name>
      <name xml:lang="en">
       <surname>Likutova</surname>
       <given-names>O. A.</given-names>
      </name>
     </name-alternatives>
     <email>olga.ku-ocean@yandex.ru</email>
     <xref ref-type="aff" rid="aff-4"/>
    </contrib>
   </contrib-group>
   <aff-alternatives id="aff-1">
    <aff>
     <institution xml:lang="ru">Shirshov Institute of Oceanology, Russian Academy of Sciences</institution>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Shirshov Institute of Oceanology, Russian Academy of Sciences</institution>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-2">
    <aff>
     <institution xml:lang="ru">Shirshov Institute of Oceanology, Russian Academy of Sciences</institution>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Shirshov Institute of Oceanology, Russian Academy of Sciences</institution>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-3">
    <aff>
     <institution xml:lang="ru">Shirshov Institute of Oceanology, Russian Academy of Sciences</institution>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Shirshov Institute of Oceanology, Russian Academy of Sciences</institution>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-4">
    <aff>
     <institution xml:lang="ru">Shirshov Institute of Oceanology, Russian Academy of Sciences</institution>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Shirshov Institute of Oceanology, Russian Academy of Sciences</institution>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <pub-date publication-format="print" date-type="pub" iso-8601-date="2025-07-20T00:00:00+03:00">
    <day>20</day>
    <month>07</month>
    <year>2025</year>
   </pub-date>
   <pub-date publication-format="electronic" date-type="pub" iso-8601-date="2025-07-20T00:00:00+03:00">
    <day>20</day>
    <month>07</month>
    <year>2025</year>
   </pub-date>
   <volume>32</volume>
   <issue>3</issue>
   <fpage>297</fpage>
   <lpage>311</lpage>
   <history>
    <date date-type="received" iso-8601-date="2025-03-03T00:00:00+03:00">
     <day>03</day>
     <month>03</month>
     <year>2025</year>
    </date>
    <date date-type="accepted" iso-8601-date="2025-03-12T00:00:00+03:00">
     <day>12</day>
     <month>03</month>
     <year>2025</year>
    </date>
   </history>
   <self-uri xlink:href="https://mhi-ras.editorum.ru/en/nauka/article/101166/view">https://mhi-ras.editorum.ru/en/nauka/article/101166/view</self-uri>
   <abstract xml:lang="ru">
    <p>Purpose. The wind wave field is non-stationary due to variability of wave formation factors such as wind action and the processes of non-linear wave interactions. However, for many practical applications, it is assumed that the wind wave process, described by some time record of waves, is quasi-stationary. Globally, there is no generally accepted length of a wave record for which the conditions of homogeneity and stationarity of the wave field would be valid. Therefore, the main purpose of the work is to estimate the interval of wave field stationarity based on the data of field contact measurements carried out in the deep-water and coastal zones of the Black Sea in different years and seasons.&#13;
Methods and Results. The data from two long-term field experiments in the Black Sea were analyzed. Waves in the open sea were measured using a Directional Waverider buoy, and in the coastal zone – a Spoondrifter Spotter buoy and a resistive string wave gauge, installed on a specialized marine trestle offshore. Spectral analysis methods were applied to the data. The spectral peak width, defined as the peakedness parameter, was used to characterize the homogeneity of wind waves. Wave records containing high values of the peakedness parameter and characterized by a narrow-band spectral distribution, were classified as the cases of quasi-stationary waves homogeneous in their spectral composition close to regular stationary waves. As a result, the characteristic time intervals were obtained for which the wave field could be assumed to be homogeneous and quasi-stationary.&#13;
Conclusions. Regardless of the conditions of wave formation, the interval of wave stationarity in the Black Sea can be taken equal to 8–12 minutes. These estimates are the same for the deep-water and coastal parts of the sea, and qualitatively correspond to the theoretical ones.</p>
   </abstract>
   <trans-abstract xml:lang="en">
    <p>Purpose. The wind wave field is non-stationary due to variability of wave formation factors such as wind action and the processes of non-linear wave interactions. However, for many practical applications, it is assumed that the wind wave process, described by some time record of waves, is quasi-stationary. Globally, there is no generally accepted length of a wave record for which the conditions of homogeneity and stationarity of the wave field would be valid. Therefore, the main purpose of the work is to estimate the interval of wave field stationarity based on the data of field contact measurements carried out in the deep-water and coastal zones of the Black Sea in different years and seasons.&#13;
Methods and Results. The data from two long-term field experiments in the Black Sea were analyzed. Waves in the open sea were measured using a Directional Waverider buoy, and in the coastal zone – a Spoondrifter Spotter buoy and a resistive string wave gauge, installed on a specialized marine trestle offshore. Spectral analysis methods were applied to the data. The spectral peak width, defined as the peakedness parameter, was used to characterize the homogeneity of wind waves. Wave records containing high values of the peakedness parameter and characterized by a narrow-band spectral distribution, were classified as the cases of quasi-stationary waves homogeneous in their spectral composition close to regular stationary waves. As a result, the characteristic time intervals were obtained for which the wave field could be assumed to be homogeneous and quasi-stationary.&#13;
Conclusions. Regardless of the conditions of wave formation, the interval of wave stationarity in the Black Sea can be taken equal to 8–12 minutes. These estimates are the same for the deep-water and coastal parts of the sea, and qualitatively correspond to the theoretical ones.</p>
   </trans-abstract>
   <kwd-group xml:lang="ru">
    <kwd>wind waves</kwd>
    <kwd>wave parameters</kwd>
    <kwd>wave record length</kwd>
    <kwd>wave field homogeneity</kwd>
    <kwd>wave spectrum</kwd>
    <kwd>stationarity interval</kwd>
   </kwd-group>
   <kwd-group xml:lang="en">
    <kwd>wind waves</kwd>
    <kwd>wave parameters</kwd>
    <kwd>wave record length</kwd>
    <kwd>wave field homogeneity</kwd>
    <kwd>wave spectrum</kwd>
    <kwd>stationarity interval</kwd>
   </kwd-group>
   <funding-group>
    <funding-statement xml:lang="ru">The study was carried out with the support of RSF, grant No. 24-27-00082</funding-statement>
    <funding-statement xml:lang="en">The study was carried out with the support of RSF, grant No. 24-27-00082</funding-statement>
   </funding-group>
  </article-meta>
 </front>
 <body>
  <p></p>
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