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 <front>
  <journal-meta>
   <journal-id journal-id-type="publisher-id">Solnechno-Zemnaya Fizika</journal-id>
   <journal-title-group>
    <journal-title xml:lang="en">Solnechno-Zemnaya Fizika</journal-title>
    <trans-title-group xml:lang="ru">
     <trans-title>Солнечно-земная физика</trans-title>
    </trans-title-group>
   </journal-title-group>
   <issn publication-format="online">2712-9640</issn>
  </journal-meta>
  <article-meta>
   <article-id pub-id-type="publisher-id">101511</article-id>
   <article-id pub-id-type="doi">10.12737/szf-121202612</article-id>
   <article-id pub-id-type="edn">rfimcx</article-id>
   <article-categories>
    <subj-group subj-group-type="toc-heading" xml:lang="ru">
     <subject>Результаты  исследований</subject>
    </subj-group>
    <subj-group subj-group-type="toc-heading" xml:lang="en">
     <subject>Results of current research</subject>
    </subj-group>
    <subj-group>
     <subject>Результаты  исследований</subject>
    </subj-group>
   </article-categories>
   <title-group>
    <article-title xml:lang="en">Critical level influence on spectra of secondary gravity waves in the middle and upper atmosphere</article-title>
    <trans-title-group xml:lang="ru">
     <trans-title>Влияние критических уровней на спектры вторичных гравитационных волн в средней и верхней атмосфере</trans-title>
    </trans-title-group>
   </title-group>
   <contrib-group content-type="authors">
    <contrib contrib-type="author">
     <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-3944-9433</contrib-id>
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Гаврилов</surname>
       <given-names>Николай Михайлович</given-names>
      </name>
      <name xml:lang="en">
       <surname>Gavrilov</surname>
       <given-names>Nikolay Mihaylovich</given-names>
      </name>
     </name-alternatives>
     <email>gannik@gmail.com</email>
     <bio xml:lang="ru">
      <p>доктор физико-математических наук;</p>
     </bio>
     <bio xml:lang="en">
      <p>doctor of physical and mathematical sciences;</p>
     </bio>
     <xref ref-type="aff" rid="aff-1"/>
    </contrib>
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Кшевецкий</surname>
       <given-names>Сергей Петрович</given-names>
      </name>
      <name xml:lang="en">
       <surname>Kshevetskii</surname>
       <given-names>Sergey Petrovich</given-names>
      </name>
     </name-alternatives>
     <email>spkshev@gmail.com</email>
     <bio xml:lang="ru">
      <p>доктор физико-математических наук;</p>
     </bio>
     <bio xml:lang="en">
      <p>doctor of physical and mathematical sciences;</p>
     </bio>
     <xref ref-type="aff" rid="aff-2"/>
     <xref ref-type="aff" rid="aff-3"/>
    </contrib>
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Коваль</surname>
       <given-names>Андрей Владиславович</given-names>
      </name>
      <name xml:lang="en">
       <surname>Koval</surname>
       <given-names>Andrey Vladislavovich</given-names>
      </name>
     </name-alternatives>
     <email>koval_spbu@mail.ru</email>
     <bio xml:lang="ru">
      <p>кандидат физико-математических наук;</p>
     </bio>
     <bio xml:lang="en">
      <p>candidate of physical and mathematical sciences;</p>
     </bio>
     <xref ref-type="aff" rid="aff-4"/>
    </contrib>
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Курдяева</surname>
       <given-names>Юлия Андреевна</given-names>
      </name>
      <name xml:lang="en">
       <surname>Kurdyaeva</surname>
       <given-names>Yulia A.</given-names>
      </name>
     </name-alternatives>
     <email>yakurdyaeva@gmail.com</email>
     <xref ref-type="aff" rid="aff-5"/>
    </contrib>
   </contrib-group>
   <aff-alternatives id="aff-1">
    <aff>
     <institution xml:lang="ru">Санкт-Петербургский государственный университет</institution>
     <city>Санкт-Петербург</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Saint-Petersburg State University</institution>
     <city>Saint Petersburg</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-2">
    <aff>
     <institution xml:lang="ru">Санкт-Петербургский государственный университет</institution>
     <city>Санкт-Петербург</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">St. Petersburg State University</institution>
     <city>Saint Petersburg</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-3">
    <aff>
     <institution xml:lang="ru">Балтийский федеральный университет имени И. Канта</institution>
     <city>Калининград</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">I. Kant Baltic Federal University</institution>
     <city>Kaliningrad</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-4">
    <aff>
     <institution xml:lang="ru">Санкт-Петербургский государственный университет</institution>
     <city>Санкт-Петербург</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Saint Petersburg State University</institution>
     <city>Saint Petersburg</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-5">
    <aff>
     <institution xml:lang="ru">Калининградский филиал Института земного магнетизма, ионосферы и распространения радиоволн им. Н.В. Пушкова РАН</institution>
     <city>Калиниград</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">West Department of Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation RAS</institution>
     <city>Kaliningrad</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <pub-date publication-format="print" date-type="pub" iso-8601-date="2026-03-25T00:00:00+03:00">
    <day>25</day>
    <month>03</month>
    <year>2026</year>
   </pub-date>
   <pub-date publication-format="electronic" date-type="pub" iso-8601-date="2026-03-25T00:00:00+03:00">
    <day>25</day>
    <month>03</month>
    <year>2026</year>
   </pub-date>
   <volume>12</volume>
   <issue>1</issue>
   <fpage>115</fpage>
   <lpage>124</lpage>
   <history>
    <date date-type="received" iso-8601-date="2025-07-19T00:00:00+03:00">
     <day>19</day>
     <month>07</month>
     <year>2025</year>
    </date>
    <date date-type="accepted" iso-8601-date="2025-10-16T00:00:00+03:00">
     <day>16</day>
     <month>10</month>
     <year>2025</year>
    </date>
   </history>
   <self-uri xlink:href="https://zh-szf.ru/en/nauka/article/101511/view">https://zh-szf.ru/en/nauka/article/101511/view</self-uri>
   <abstract xml:lang="ru">
    <p>С помощью нелинейной численной модели высокого разрешения исследуется распространение внутренних гравитационных волн (ВГВ) из тропосферы в верхние слои атмосферы. В этом моделировании учитываются фоновые профили ветра, содержащие критические уровни, на которых горизонтальная скорость ветра становится равной горизонтальной фазовой скорости ВГВ. Согласно традиционной линейной теории атмосферных волн, вблизи критических уровней вертикальная длина волны приближается к нулю, что должно приводить к сильной диссипации ВГВ, распространяющихся из тропосферы, и может сильно уменьшить их амплитуды в верхней атмосфере. Модельные источники волн заданы в виде возмущений вертикальной скорости, распространяющихся вдоль поверхности Земли. Горизонтальный ветер в атмосфере аппроксимируется гауссовым профилем среднего зонального ветра с максимумом на высоте 50 км. Выполнен анализ спектров волновых полей вблизи критических уровней и на удалении от них. Обнаружено, что неустойчивость волн около критических уровней интенсифицирует переход энергии от первичных ВГВ, распространяющихся от приземных источников, к вторичным волновым модам. Это приводит к росту спектральных пиков на длинах волн меньших горизонтальной длины первичной ВГВ. Поэтому выше критических уровней с ростом высоты начинают преобладать режимы с более короткими горизонтальными длинами волн, чем длина волны первичной ВГВ, причем амплитуды этих вторичных волн на той же высоте могут превышать амплитуды аналогичной первичной ВГВ, распространяющейся в случае отсутствия критических уровней в средней атмосфере.</p>
   </abstract>
   <trans-abstract xml:lang="en">
    <p>A high-resolution nonlinear numerical model is used to simulate propagation of internal gravity waves (IGWs) from the troposphere to the upper atmosphere. This simulation takes into account background wind profiles containing critical levels at which the horizontal wind velocity becomes equal to the horizontal phase speed of IGW. According to traditional linear theories of atmospheric waves, near critical levels the vertical wavelength approaches zero, which should lead to a strong dissipation of IGWs propagating from the troposphere and may significantly decrease their amplitudes in the upper atmosphere. The wave sources in the model are defined as vertical velocity perturbations propagating along the Earth surface. The mean horizontal wind in the atmosphere is approximated by the Gaussian profile with a maximum at an altitude of 50 km. We analyze the spectra of wave fields near critical levels and at a distance from them. It has been found that the instability of waves near critical levels intensifies the energy transition from primary IGWs propagating from surface sources to secondary wave modes. This causes an increase in spectral peaks at wavelengths shorter than the horizontal length of primary IGW. Therefore, above critical levels, spectral modes with shorter horizontal wavelengths begin to prevail with increasing altitude, and the amplitudes of these secondary waves at the same altitudes can exceed the amplitudes of analogous primary IGW propagating in the absence of critical levels in the middle atmosphere.</p>
   </trans-abstract>
   <kwd-group xml:lang="ru">
    <kwd>акустико-гравитационные волны</kwd>
    <kwd>спектр</kwd>
    <kwd>вторичные волны</kwd>
    <kwd>численное моделирование</kwd>
    <kwd>верхняя атмосфера</kwd>
    <kwd>средняя атмосфера</kwd>
   </kwd-group>
   <kwd-group xml:lang="en">
    <kwd>acoustic-gravity waves</kwd>
    <kwd>spectrum</kwd>
    <kwd>secondary waves</kwd>
    <kwd>numerical simulation</kwd>
    <kwd>upper atmosphere</kwd>
    <kwd>middle atmosphere</kwd>
   </kwd-group>
   <funding-group>
    <funding-statement xml:lang="ru">Данное исследование выполнено при финансовой поддержке Российского научного фонда (грант № 25-17-00166)</funding-statement>
    <funding-statement xml:lang="en">This research was financially supported by the Russian Science Foundation (Grant No. 25-17-00166)</funding-statement>
   </funding-group>
  </article-meta>
 </front>
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