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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">hydrophysics</journal-id><journal-title-group><journal-title xml:lang="ru">Фундаментальная и прикладная гидрофизика</journal-title><trans-title-group xml:lang="en"><trans-title>Fundamental and Applied Hydrophysics</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2073-6673</issn><issn pub-type="epub">2782-5221</issn><publisher><publisher-name>St. Petersburg Research Center of the Russian Academy of Sciences</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.7868/S2073667321020027</article-id><article-id custom-type="elpub" pub-id-type="custom">hydrophysics-64</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>ГИДРОФИЗИЧЕСКИЕ И БИОГЕОХИМИЧЕСКИЕ ПОЛЯ И ПРОЦЕССЫ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>HYDROPHYSICAL AND BIOGEOCHEMICAL FIELDS AND PROCESSES</subject></subj-group></article-categories><title-group><article-title>Расчет турбулентных напряжений в конвективно-перемешанном слое в мелководном озере подо льдом с использованием двух ADCP</article-title><trans-title-group xml:lang="en"><trans-title>Deriving of Turbulent Stresses in a Convectively Mixed Layer in a Shallow Lake Under Ice by Coupling Two ADCPs</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Богданов</surname><given-names>С. Р.</given-names></name><name name-style="western" xml:lang="en"><surname>Bogdanov</surname><given-names>S. R.</given-names></name></name-alternatives><bio xml:lang="ru"><p>185030, пр. Александра Невского, д. 50, г. Петрозаводск</p></bio><bio xml:lang="en"><p>185030, Aleksandra Nevskogo Pr., 50, Petrozavodsk</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Здоровеннов</surname><given-names>Р. Э.</given-names></name><name name-style="western" xml:lang="en"><surname>Zdorovennov</surname><given-names>R. E.</given-names></name></name-alternatives><bio xml:lang="ru"><p>185030, пр. Александра Невского, д. 50, г. Петрозаводск</p></bio><bio xml:lang="en"><p>185030, Aleksandra Nevskogo Pr., 50, Petrozavodsk</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Пальшин</surname><given-names>Н. И.</given-names></name><name name-style="western" xml:lang="en"><surname>Palshin</surname><given-names>N. I.</given-names></name></name-alternatives><bio xml:lang="ru"><p>185030, пр. Александра Невского, д. 50, г. Петрозаводск</p></bio><bio xml:lang="en"><p>185030, Aleksandra Nevskogo Pr., 50, Petrozavodsk</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Здоровеннова</surname><given-names>Г. Э.</given-names></name><name name-style="western" xml:lang="en"><surname>Zdorovennova</surname><given-names>G. E.</given-names></name></name-alternatives><bio xml:lang="ru"><p>185030, пр. Александра Невского, д. 50, г. Петрозаводск</p></bio><bio xml:lang="en"><p>185030, Aleksandra Nevskogo Pr., 50, Petrozavodsk</p></bio><email xlink:type="simple">zdorovennova@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Тержевик</surname><given-names>А. Ю.</given-names></name><name name-style="western" xml:lang="en"><surname>Terzhevik</surname><given-names>A. Yu.</given-names></name></name-alternatives><bio xml:lang="ru"><p>185030, пр. Александра Невского, д. 50, г. Петрозаводск</p></bio><bio xml:lang="en"><p>185030, Aleksandra Nevskogo Pr., 50, Petrozavodsk</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Гавриленко</surname><given-names>Г. Г.</given-names></name><name name-style="western" xml:lang="en"><surname>Gavrilenko</surname><given-names>G. G.</given-names></name></name-alternatives><bio xml:lang="ru"><p>185030, пр. Александра Невского, д. 50, г. Петрозаводск</p></bio><bio xml:lang="en"><p>185030, Aleksandra Nevskogo Pr., 50, Petrozavodsk</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Волков</surname><given-names>С. Ю.</given-names></name><name name-style="western" xml:lang="en"><surname>Volkov</surname><given-names>S. Yu.</given-names></name></name-alternatives><bio xml:lang="ru"><p>185030, пр. Александра Невского, д. 50, г. Петрозаводск</p></bio><bio xml:lang="en"><p>185030, Aleksandra Nevskogo Pr., 50, Petrozavodsk</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Ефремова</surname><given-names>Т. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Efremova</surname><given-names>T. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>185030, пр. Александра Невского, д. 50, г. Петрозаводск</p></bio><bio xml:lang="en"><p>185030, Aleksandra Nevskogo Pr., 50, Petrozavodsk</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Кулдин</surname><given-names>Н. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Kuldin</surname><given-names>N. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>185910, пр. Ленина, д. 33, г. Петрозаводск</p></bio><bio xml:lang="en"><p>185910, Lenina Pr., 33, Petrozavodsk</p></bio><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Кириллин</surname><given-names>Г. Б.</given-names></name><name name-style="western" xml:lang="en"><surname>Kirillin</surname><given-names>G. B.</given-names></name></name-alternatives><bio xml:lang="ru"><p>12587 Mюггельзеедамм, 310, г. Берлин</p></bio><bio xml:lang="en"><p>12587, Müggelseedamm, 310, Berlin</p></bio><xref ref-type="aff" rid="aff-3"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Институт водных проблем Севера КарНЦ РАН</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Northern Water Problems Institute Karelian Research Center of RAS</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Петрозаводский государственный университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Petrozavodsk State University</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-3"><aff xml:lang="ru"><institution>Лейбниц-Институт пресноводной экологии и рыболовства внутренних водоемов</institution><country>Германия</country></aff><aff xml:lang="en"><institution>Department of Ecohydrology, Leibniz-Institute of Freshwater Ecology and Inland Fisheries (IGB)</institution><country>Germany</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2021</year></pub-date><pub-date pub-type="epub"><day>29</day><month>11</month><year>2021</year></pub-date><volume>14</volume><issue>2</issue><fpage>17</fpage><lpage>28</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Богданов С.Р., Здоровеннов Р.Э., Пальшин Н.И., Здоровеннова Г.Э., Тержевик А.Ю., Гавриленко Г.Г., Волков С.Ю., Ефремова Т.В., Кулдин Н.А., Кириллин Г.Б., 2021</copyright-statement><copyright-year>2021</copyright-year><copyright-holder xml:lang="ru">Богданов С.Р., Здоровеннов Р.Э., Пальшин Н.И., Здоровеннова Г.Э., Тержевик А.Ю., Гавриленко Г.Г., Волков С.Ю., Ефремова Т.В., Кулдин Н.А., Кириллин Г.Б.</copyright-holder><copyright-holder xml:lang="en">Bogdanov S.R., Zdorovennov R.E., Palshin N.I., Zdorovennova G.E., Terzhevik A.Y., Gavrilenko G.G., Volkov S.Y., Efremova T.V., Kuldin N.A., Kirillin G.B.</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://hydrophysics.spbrc.ru/jour/article/view/64">https://hydrophysics.spbrc.ru/jour/article/view/64</self-uri><abstract><p>Представлен метод расчета турбулентных напряжений, основанный на использовании пары трехлучевых акустических допплеровских профилографов скорости, c одной или двумя точками пересечения лучей. Для апробации метода был спланирован и проведен специальный натурный эксперимент по измерению температуры воды, уровня подледной облученности и компонент скорости в конвективно-перемешанном слое покрытого льдом небольшого бореального озера. Полученные данные позволяют рассчитать не только интенсивности пульсаций вдоль трех ортогональных осей, но и недиагональные компоненты тензора Рейнольдса. С использованием условия однородности средней скорости по горизонтали получены количественные результаты, описывающие энергетику процессов в период весенней подледной конвекции: рассчитана анизотропия турбулентных пульсаций, изучена корреляция энергии турбулентности с интенсивностью накачки (через поток плавучести). Приведен качественный анализ параметров и динамики энергосодержащих структур, развивающихся в конвективном слое небольших покрытых льдом озер весной.</p></abstract><trans-abstract xml:lang="en"><p>This paper presents a method for deriving turbulent stresses using a pair of ADCPs with one or two points of beam intersections. A specific experiment, which includes measurements of water temperature, under-ice irradiation levels, and velocity components in the convectively mixed layer of a shallow ice-covered boreal lake, validated the method. The experimental data allows calculations of both the pulsation intensities along the three orthogonal axes and off-diagonal components of the Reynolds tensor. The specific features of spring under-ice convection processes, in particular, the anisotropy of turbulent pulsations and the correlation of turbulence energy with the turbulence energy production (as the buoyancy flux), were described using the horizontal homogeneity assumption. Finally, the paper presents a qualitative analysis of the parameters and dynamics of energy-containing structures developing in the convective layer of small ice-covered lakes in spring.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>бореальное озеро</kwd><kwd>температура воды</kwd><kwd>подледная радиация</kwd><kwd>поток плавучести</kwd><kwd>скорости течений</kwd><kwd>конвективно-перемешанный слой</kwd><kwd>акустические допплеровские профилографы</kwd><kwd>тензор турбулентных напряжений</kwd><kwd>анизотропия турбулентных пульсаций</kwd></kwd-group><kwd-group xml:lang="en"><kwd>boreal lake</kwd><kwd>water temperature</kwd><kwd>under-ice radiation</kwd><kwd>buoyancy flux</kwd><kwd>current velocities</kwd><kwd>convectively mixed layer</kwd><kwd>acoustic Doppler profilers</kwd><kwd>turbulent stress tensor</kwd><kwd>anisotropy of turbulent pulsations</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Howarth M.J., Souza A.J. 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