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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">geomorf</journal-id><journal-title-group><journal-title xml:lang="ru">Геоморфология и палеогеография</journal-title><trans-title-group xml:lang="en"><trans-title>Geomorfologiya i Paleogeografiya</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2949-1789</issn><issn pub-type="epub">2949-1797</issn><publisher><publisher-name></publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.31857/10.7868/S2949179726030028</article-id><article-id custom-type="elpub" pub-id-type="custom">geomorf-3748</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>Экзогенная геоморфология</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>Earth surface processes and landforms</subject></subj-group></article-categories><title-group><article-title>Гидравлическое обоснование формирования выработанного продольного профиля аллювиальных русел</article-title><trans-title-group xml:lang="en"><trans-title>Hydraulic justification of the formation of the adjusted longitudinal profile of alluvial channels</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>Сидорчук</surname><given-names>А. Ю.</given-names></name><name name-style="western" xml:lang="en"><surname>Sidorchuk</surname><given-names>A. Yu.</given-names></name></name-alternatives><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Московский государственный университет имени М. В. Ломоносова, географический факультет, Москва</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Lomonosov Moscow State University, Faculty of Geography, Moscow</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2026</year></pub-date><pub-date pub-type="epub"><day>14</day><month>09</month><year>2026</year></pub-date><volume>57</volume><issue>3</issue><fpage>424</fpage><lpage>437</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Сидорчук А.Ю., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Сидорчук А.Ю.</copyright-holder><copyright-holder xml:lang="en">Sidorchuk A.Y.</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://geomorphology.igras.ru/jour/article/view/3748">https://geomorphology.igras.ru/jour/article/view/3748</self-uri><abstract><p>При выработанном продольном профиле в динамически-устойчивом аллювиальном речном русле отсутствуют однонаправленные изменения отметок дна за длительный период времени. Условием существования такого продольного профиля являются неизменность величины расхода руслообразующих наносов вдоль каждого бесприточного участка реки и увеличение этого расхода в каждом узле слияния на величину расхода руслообразующих наносов в притоке. Поэтому для замыкания и решения системы уравнений гидравлики для построения выработанного продольного профиля используется формула для расчета расхода руслообразующих наносов, дополненная гипотезой о неизменности их концентрации в речном бассейне. Уклоны рассчитанного таким образом профиля русла уменьшаются с ростом максимальных расходов воды и возрастают с увеличением крупности и концентрации руслообразующих наносов, а также шероховатости русла. Построение выработанного продольного профиля реки имеет как теоретическое, так и практическое значение. На равнинных реках с небольшим стоком наносов формирование выработанного профиля русла занимает десятки тысяч лет, и здесь интерес может представлять оценка палеогидрологических условий, при которых такой профиль образовался. Например, по форме продольного профиля второй террасы р. Оки рассчитаны сток воды, который был в два раза меньше современного и сток наносов, превосходивший современный в четыре раза. На реках с большим стоком наносов, таких как р. Терек в низовьях, стабильный профиль вырабатывается за несколько десятков лет. Здесь практически важным становится регулирование формы продольного профиля и приведение его к выработанному для стабилизации русловых переформирований.</p></abstract><trans-abstract xml:lang="en"><p>In the adjusted longitudinal profile, there are no unidirectional changes in the bed elevations in the alluvial river channel over a long period of time. The prerequisite for the existence of such a longitudinal profile is the constant bedload transport rate along each section of the river without tributaries and its increase at each confluence with a tributary by the amount of the bedload discharge in this tributary. Therefore, to close and solve the system of hydraulic equations for constructing the adjusted longitudinal profile, a formula for calculating bedload transport rate is used, supplemented by the hypothesis of its constant value in the river basin. The inclination of the channel profile calculated in this way decrease with an increase in the maximum discharge and increase with an increase in the particle size and the concentration of the bedload sediments, and the channel bed roughness. Constructing an adjusted longitudinal profile of the river has both theoretical and practical significance. In lowland rivers with low sediment loads, the formation of an adjusted channel profile takes tens of thousands of years, and here it may be of interest to assess the paleohydrological conditions under which such a profile was formed. For example, based on the longitudinal profile of the second terrace of the Oka River, annual water flow was calculated to be half of what it is today, while sediment yield was four times greater than today. In rivers with high sediment loads, such as the lower reaches of the Terek River, the adjusted profile develops over several decades. Here, it becomes practically important to regulate the shape of the longitudinal profile and bring it into line with the adjusted one in order to stabilize channel transformations.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>русловые переформирования</kwd><kwd>динамически-устойчивое русло</kwd><kwd>концентрация руслообразующих наносов</kwd><kwd>уравнения гидравлики</kwd><kwd>вторая терраса р. Оки</kwd><kwd>русло р. Терек в низовьях</kwd></kwd-group><kwd-group xml:lang="en"><kwd>channel transformations</kwd><kwd>dynamically stable channel</kwd><kwd>concentration of bedload sediments</kwd><kwd>hydraulic equations</kwd><kwd>second terrace of the Oka River</kwd><kwd>channel of the Terek River in the lower reaches</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">Асеев А.А. (1959) Палеогеография долины средней и нижней Оки в четвертичный период. М.: Изд-во АН СССР. 201 с.</mixed-citation><mixed-citation xml:lang="en">Alekseevsky N.I., Mikhailov V.N., Sidorchuk A.Yu. (1993) Formation of the modern mouth section of the Terek River. In: Kaspiyskoye more. Gidrologiya ust'yev rek Tereka i Sulaka (Caspian Sea. Hydrology of the Terek and Sulak River estuaries). Moscow: Nauka (Publ.). P. 51–69 (in Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Алексеевский Н.И., Михайлов В.Н., Сидорчук А.Ю. (1993) Формирование современного устьевого участка р. Терека. В сб.: Каспийское море. Гидрология устьев рек Терека и Сулака. М.: Наука. С. 51–69.</mixed-citation><mixed-citation xml:lang="en">Alekseevsky N.I., Sidorchuk A.Yu. (1993) Expected changes in the longitudinal profile of the channel at the mouth of the Terek River. In: Kaspiyskoye more. Gidrologiya ust'yev rek Tereka i Sulaka (Caspian Sea. Hydrology of the Terek and Sulak River estuaries). Moscow: Nauka (Publ.). P. 135–144 (in Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Алексеевский Н.И., Сидорчук А.Ю. (1993) Ожидаемые изменения продольного профиля русла на устьевом участке р. Терека. В сб.: Каспийское море. Гидрология устьев рек Терека и Сулака. М.: Наука. С. 135–144.</mixed-citation><mixed-citation xml:lang="en">Arkesteijn L., Blom A., Czapiga M.J., Chavarrías V., Labeur R.J. (2019) The quasi-equilibrium longitudinal profile in backwater reaches of the engineered alluvial river: A space-marching method. J. Geophys. Res. Earth Surf. Vol. 124. https://doi.org/10.1029/2019JF005195</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Богомолов А.И., Михайлов К.А. (1972) Гидравлика. М.: Стройиздат. 648 с.</mixed-citation><mixed-citation xml:lang="en">Aseev A.A. (1959) Paleogeografiya doliny sredney i nizhney Oki v chetvertichny period (Paleogeography of the middle and lower Oka valley in the Quaternary period). Moscow: USSR Acad. of Sci. (Publ.). 201 p. (in Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Болиг А. (1956) Очерки по геоморфологии. М.: Издательство иностранной литературы. 262 с.</mixed-citation><mixed-citation xml:lang="en">Baulig H. (1956) Ocherki geomorfologii (Essays on Geomorphology). Moscow: Inostrannaya Literatura (Publ.). 262 p. (in Russ).</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Бутаков Г.П. (1986) Плейстоценовый перигляциал на востоке Русской равнины. Казань: Изд-во КГУ. 144 с. Гришанин К.В. (1979) Динамика русловых потоков. Л.: Гидрометеоиздат. 311 с.</mixed-citation><mixed-citation xml:lang="en">Blom A., Arkesteijn L., Chavarrías Borras V., Viparelli E. (2017) The equilibrium alluvial river under variable flow and its channel-forming discharge. J. Geophys. Res. Earth Surf. Vol. 122. P. 1924–1948. https://doi.org/10.1002/2017JF004213.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Завадский А.С., Самохин М.А., Чалов С.Р. и др. (2024) Современная морфодинамика основного дельтового рукава р. Терек (Каргалинский Прорыв). Эрозия почв и русловые процессы. № 1. С. 87–106. https://doi.org/10.71367/3034-4638-2024-1-1-87-106</mixed-citation><mixed-citation xml:lang="en">Blom A., Viparelli E., Chavarrías V. (2016) The graded alluvial river: Profile concavity and downstream fining. Geophys. Res. Lett. Vol. 43. P. 6285–6293. doi:10.1002/2016GL068898</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Караушев А.В. (1977) Теория и методы расчетов речных наносов. Л.: Гидрометеоиздат. 272 с.</mixed-citation><mixed-citation xml:lang="en">Bogomolov A.I., Mikhailov K.A. (1972) Gidravlika (Hydraulics). Ed. 2: revised and supplemented edition. Moscow: Stroyizdat (Publ.). 648 p. (in Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Кузьмин И.А. (2012) Общая методология изучения и прогнозирования русловых процессов. М.: Волшебный фонарь. 304 с.</mixed-citation><mixed-citation xml:lang="en">Bolla Pittaluga M., Luchi R., Seminara G. (2014) On the equilibrium profile of river beds. J. Geophys. Res. Earth Surf. Vol. 119. P. 317–332. doi:10.1002/2013JF002806</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Куприянов В.В. (ред.) (1973) Ресурсы поверхностных вод СССР. Северный Кавказ. Т. 8. Л.: Гидрометеоиздат. 446 с.</mixed-citation><mixed-citation xml:lang="en">Davis W.M. (1902) Base level, grade, and peneplain. J. Geol. Vol. 10. P. 77–111.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Маккавеев Н.И. (1955) Русло реки и эрозия в ее бассейне. М.: Изд-во АН СССР. 346 с.</mixed-citation><mixed-citation xml:lang="en">Exner F.M. (1920) Zur physik der dünen. Akad. Wiss. Wien Math. Naturwiss. Klasse. Vol. 129 (2a). P. 929–952. (in German).</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Маккавеев Н.И. (ред.) (1964) Проектирование судовых ходов на свободных реках. М.: Транспорт. 263 с.</mixed-citation><mixed-citation xml:lang="en">Grishanin K.V. (1979) Dinamika ruslovykh potokov (Dynamics of channel flows). Leningrad: Gidrometeoizdat (Publ.). 311 p. (in Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Марков К.К. (1948) Основные проблемы геоморфологии. М.: Географгиз. 344 с.</mixed-citation><mixed-citation xml:lang="en">Huang H.Q., Chang H.H. (2006) Scale independent linear behaviour of alluvial channel flow. J. Hydraulic Engineering. Vol. 132. P. 722–730.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Мирцхулава Ц.Е. (1970) Инженерные методы расчета и прогноза водной эрозии. М.: Колос. 240 с.</mixed-citation><mixed-citation xml:lang="en">Kupriyanov V.V. (ed.) (1973) Resursy poverkhnostnykh vod SSSR. Severnyi Kavkaz (Surface Water Resources of the USSR. North Caucasus). Vol. 8. Leningrad: Gidrometeoizdat (Publ.). 446 p. (in Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Никулин А.С., Поволоцкий М.Я., Сидорчук А.Ю. (1989) Изменение пропускной способности русла в низовьях р. Терек. Водные ресурсы. № 6. С. 56–61.</mixed-citation><mixed-citation xml:lang="en">Kuzmin I.A. (2012) Obshchaya metodologiya izucheniya i prognozirovaniya ruslovykh protsessov (General methodology for studying and forecasting channel processes). Moscow: Volshebnyi fonar' (Publ.). 304 p. (in Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Сидорчук А.Ю. (2025а) Процессы формирования продольного профиля реки. Геоморфология и палеогеография. Т. 56. № 2. С. 185–196.</mixed-citation><mixed-citation xml:lang="en">Leopold L.B., Maddock T. (1953). The hydraulic geometry of stream channels and some physiographic implications. US Geological Survey Professional Paper 252. Washington, DC: US Government Printing Office. 64 p.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Сидорчук А.Ю. (2025б) Формирование продольного профиля реки при существенном влиянии склоновых процессов (на примере р. Ваипаоа, Новая Зеландия). Геоморфология и палеогеография. Т. 56. № 3. С. 359–371.</mixed-citation><mixed-citation xml:lang="en">Mackin J.H. (1948) Concept of the graded river. Geological Society of America Bulletin. Vol. 59. P. 463–512.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Сидорчук А.Ю., Панин А.В., Борисова О.К. (2008) Климатически обусловленные изменения речного стока на равнинах Северной Евразии в позднеледниковье и голоцене. Водные ресурсы. Т. 35. № 4. С. 406–416.</mixed-citation><mixed-citation xml:lang="en">Makkaveev N.I. (1955) Ruslo reki i eroziya v ee basseine (River bed and erosion in its basin). Moscow: AN SSSR (Publ.). 346 p. (in Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Сидорчук А.Ю., Борисова О.К., Панин А.В. (2025) Морфология русел и водный режим больших рек равнин Северной Евразии 14–18 тысяч лет назад. Эрозия почв и русловые процессы. № 4. С. 58–98. https://doi.org/10.71367/3034-4638-2025-4-4-58-98</mixed-citation><mixed-citation xml:lang="en">Makkaveev N.I. (Ed.) (1964) Proyektirovaniye sudovykh khodov na svobodnykh rekakh (Design of the navigation routes on free rivers). Moscow: Transport (Publ.). 263 p. (in Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Тимофеев Д.А. (1981) Терминология флювиальной геоморфологии: материалы по геоморфологической терминологии. М.: Наука. 268 с.</mixed-citation><mixed-citation xml:lang="en">Markov K.K. (1948) Osnovnye problemy geomorfologii (Basic problems of geomorphology). Moscow: Geografgiz (Publ.). 344 p. (in Russ).</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Трофимов А.М., Московкин В.М. (1982) Моделирование устойчивой системы река–канал. География и природные ресурсы. № 4. С. 101–107.</mixed-citation><mixed-citation xml:lang="en">Nanson G.C., Huang H.Q. (2008) Least action principle, equilibrium states, iterative adjustment and the stability of alluvial channels. Earth Surf. Process. Landforms. Vol. 33. P. 923–942. https://doi.org/10.1002/esp.1584</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Чижов О.П. (1951) Опыт построения продольного профиля реки, исходя из основных условий, определяющих его форму. Метеорология и гидрология. № 7. С. 20–24.</mixed-citation><mixed-citation xml:lang="en">Nikulin A.S., Povolotsky M.Ya., Sidorchuk A.Yu. (1989) Changes in the channel capacity in the lower reaches of the Terek River. Vodnyye resursy. No. 6. P. 56–61 (in Russ).</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Чоу В.Т. (1969) Гидравлика открытых каналов. М.: Стройиздат. 464 с.</mixed-citation><mixed-citation xml:lang="en">Rhoads B.L. (2020) The vertical dimension of rivers: Longitudinal profiles, profile adjustments, and step-pool morphology. In: River Dynamics: Geomorphology to Support Management. Cambridge, UK: Cambridge University Press. P. 294–318.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Щукин И.С. (1980) Четырехъязычный энциклопедический словарь терминов по физической географии: русско-англо-немецко-французский. М.: Советская энциклопедия. 703 с.</mixed-citation><mixed-citation xml:lang="en">Shchukin I.S. (1980) Chetyrekh"yazychnyy entsiklopedicheskiy slovar' terminov po fizicheskoy geografii: Rus.-angl.-nem.-fr. (Four-language encyclopedic dictionary of terms on physical geography: Russian-English-German-French). Moscow: Sovetskaya entsiklopediya (Publ.). 703 p.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Яблоков Ю.Е. (ред.) (1973) Ресурсы поверхностных вод СССР. Верхне-Волжский район. Т. 10. Л.: Гидрометеоиздат. 475 с.</mixed-citation><mixed-citation xml:lang="en">Sidorchuk A.Yu., Panin A.V., Borisova O.K. (2018) River runoff on the East European Plain over the past 20 thousand years and the problem of changing levels of the southern seas. Voprosy geografii. Iss. 145. Hydrological changes. Moscow: Publishing House "Kodeks". P. 144–168. (in Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Arkesteijn L., Blom A., Czapiga M.J. et al. (2019) The quasi- equilibrium longitudinal profile in backwater reaches of the engineered alluvial river: A space-marching method. J. Geophys. Res.: Earth Surf. Vol. 124. Iss. 11. P. 2542–2560. https://doi.org/10.1029/2019JF005195</mixed-citation><mixed-citation xml:lang="en">Stock J.D., Montgomery D.R., Collins B.D., Dietrich W.E., Sklar L.S. (2005) Field measurements of incision rates following bedrock exposure: Implications for process controls on the long profiles of valleys cut by river debris flows. Geological Society of America Bulletin. Vol. 117. Iss. 11/12. P. 174–194.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Blom A., Arkesteijn L., Chavarrías Borras V., Viparelli E. (2017) The equilibrium alluvial river under variable flow and its channel-forming discharge. J. Geophys. Res.: Earth Surf. Vol. 122. Iss. 10. P. 1924–1948. https://doi.org/10.1002/2017JF004213</mixed-citation><mixed-citation xml:lang="en">Timofeev D.A. (1981) Terminologiya flyuvial'noy geomorfologii: materialy po geomorfologicheskoy terminologii (Terminology of fluvial geomorphology: materials on geomorphological terminology). Moscow: Nauka (Publ.). 268 p. (in Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Blom A., Viparelli E., Chavarrías V. (2016) The graded alluvial river: Profile concavity and downstream fining. Geophys. Res. Lett. Vol. 43. Iss. 12. P. 6285–6293. https://doi.org/10.1002/2016GL068898</mixed-citation><mixed-citation xml:lang="en">Trofimov A.M., Moskovkin V.M. (1982) Modeling of a stable river-canal system. Geografiya i prirodnye resursy. No. 4. P. 101–107 (in Russ).</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Bolla Pittaluga M., Luchi R., Seminara G. (2014) On the equilibrium profile of river beds. J. Geophys. Res.: Earth Surf. Vol. 119. Iss. 2. P. 317–332. https://doi.org/10.1002/2013JF002806</mixed-citation><mixed-citation xml:lang="en">Whipple K.X., Tucker G.E. (1999) Dynamics of the stream-power river incision model: Implications for height limits of mountain ranges, landscape response timescales, and research needs. J. Geophys. Res. Vol. 104. Iss. B8. P. 17661–17674. https://doi.org/10.1029/1999JB900120</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Davis W.M. (1902) Baselevel, grade, and peneplain. J. of Geology. Vol. 10. P. 77–111.</mixed-citation><mixed-citation xml:lang="en">Wolman M.G., Miller J.P. (1960) Magnitude and frequency of forces in geomorphic processes. The Journal of Geology. Vol. 68. P. 54–74.</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Exner F.M. (1920) Zur physik der dünen. Akad. Wiss. Wien Math. Naturwiss. Klasse. Vol. 129 (2a). P. 929–952. Huang H.Q., Chang H.H. (2006) Scale independent linear behaviour of alluvial channel f low. J. of Hydraulic Engineering. Vol. 132. P. 722–730.</mixed-citation><mixed-citation xml:lang="en">Yablokov Yu.E. (ed.) (1973) Resursy poverkhnostnykh vod SSSR. Verkhne-Volzhskiy rayon (Surface Water Resources of the USSR. Upper Volga Region). Vol. 10. Leningrad: Gidrometeoizdat (Publ.). 475 p. (in Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Leopold L.B., Maddock T. (1953). The hydraulic geometry of stream channels and some physiographic implications. US Geological Survey Professional. Paper 252. Washington, DC: US Government Printing Office. 64 p. https://doi.org/10.3133/pp252</mixed-citation><mixed-citation xml:lang="en">Leopold L.B., Maddock T. (1953). The hydraulic geometry of stream channels and some physiographic implications. US Geological Survey Professional. Paper 252. Washington, DC: US Government Printing Office. 64 p. https://doi.org/10.3133/pp252</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Mackin J.H. (1948) Concept of the graded river. Geol. Soc. Am. Bull. Vol. 59. P. 463–511.</mixed-citation><mixed-citation xml:lang="en">Mackin J.H. (1948) Concept of the graded river. Geol. Soc. Am. Bull. Vol. 59. P. 463–511.</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">Nanson G.C., Huang H.Q. (2008) Least action principle, equilibrium states, iterative adjustment and the stability of alluvial channels. Earth Surf. Processes Landforms. Vol. 33. Iss. 6. P. 923–942. https://doi.org/10.1002/esp.1584</mixed-citation><mixed-citation xml:lang="en">Nanson G.C., Huang H.Q. (2008) Least action principle, equilibrium states, iterative adjustment and the stability of alluvial channels. Earth Surf. Processes Landforms. Vol. 33. Iss. 6. P. 923–942. https://doi.org/10.1002/esp.1584</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">Rhoads B.L. (2020) Chapter 13 – The vertical dimension of rivers: Longitudinal profiles, profile adjustments, and step-pool morphology. In: River Dynamics: Geomorphology to Support Management. Cambridge, UK: Cambridge University Press. P. 294–318. https://doi.org/10.1017/9781108164108.013</mixed-citation><mixed-citation xml:lang="en">Rhoads B.L. (2020) Chapter 13 – The vertical dimension of rivers: Longitudinal profiles, profile adjustments, and step-pool morphology. In: River Dynamics: Geomorphology to Support Management. Cambridge, UK: Cambridge University Press. P. 294–318. https://doi.org/10.1017/9781108164108.013</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">Stock J.D., Montgomery D.R., Collins B.D. et al. (2005) Field measurements of incision rates following bedrock exposure: Implications for process controls on the long profiles of valleys cut by river debris flows. Geol. Soc. Am. Bull. Vol. 117. No. 11/12. P. 174–194. https://doi.org/10.1130/B25560.1</mixed-citation><mixed-citation xml:lang="en">Stock J.D., Montgomery D.R., Collins B.D. et al. (2005) Field measurements of incision rates following bedrock exposure: Implications for process controls on the long profiles of valleys cut by river debris flows. Geol. Soc. Am. Bull. Vol. 117. No. 11/12. P. 174–194. https://doi.org/10.1130/B25560.1</mixed-citation></citation-alternatives></ref><ref id="cit37"><label>37</label><citation-alternatives><mixed-citation xml:lang="ru">Whipple K.X., Tucker G.E. (1999) Dynamics of the stream-power river incision model: Implications for height limits of mountain ranges, landscape response timescales, and research needs. J. Geophys. Res. Vol. 104. Iss. B8. P. 17661–17674. https://doi.org/10.1029/1999JB900120</mixed-citation><mixed-citation xml:lang="en">Whipple K.X., Tucker G.E. (1999) Dynamics of the stream-power river incision model: Implications for height limits of mountain ranges, landscape response timescales, and research needs. J. Geophys. Res. Vol. 104. Iss. B8. P. 17661–17674. https://doi.org/10.1029/1999JB900120</mixed-citation></citation-alternatives></ref><ref id="cit38"><label>38</label><citation-alternatives><mixed-citation xml:lang="ru">Wolman M.G., Miller J.P. (1960) Magnitude and frequency of forces in geomorphic processes. J. of Geology. Vol. 68. No. 1. P. 54–74. https://doi.org/10.1086/626637</mixed-citation><mixed-citation xml:lang="en">Wolman M.G., Miller J.P. (1960) Magnitude and frequency of forces in geomorphic processes. J. of Geology. Vol. 68. No. 1. P. 54–74. https://doi.org/10.1086/626637</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
