Peculiarities of the dynamics of a viscous liquid with a free boundary under periodic influences
Purpose of the work is revealing and researching of peculiarities of a motion of a viscous liquid having a free boundary and undergoing periodic in time influences which are characterized by the absence of a predominant direction in space. Methods. The analytic investigation methods of non-linear p...
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| Format: | Article |
| Language: | English |
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Saratov State University
2024-03-01
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| Series: | Известия высших учебных заведений: Прикладная нелинейная динамика |
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| Online Access: | https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2024/03/and_2024-2_sennitskii_197-208.pdf |
| _version_ | 1797235628940722176 |
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| author | Sennitskii, Vladimir Leonidovich |
| author_facet | Sennitskii, Vladimir Leonidovich |
| author_sort | Sennitskii, Vladimir Leonidovich |
| collection | DOAJ |
| description | Purpose of the work is revealing and researching of peculiarities of a motion of a viscous liquid having a free boundary and undergoing periodic in time influences which are characterized by the absence of a predominant direction in space. Methods. The analytic investigation methods of non-linear problems, of boundary problems for the system of Navier– Stokes and continuity equations are used that are the method of perturbations (the method of a small parameter) the method of Fourier (the method of a separation of variables), an averaging, a construction and studying of asymptotic formulas. Results. A new problem on the motion of a viscous liquid is formulated and solved. Asymptotic representations of the found solution are constructed and explored. New hydromechanical effects are revealed. Conclusion. The work is fulfilled in the development of a perspective direction in liquid mechanics that is of researching the dynamics of hydromechanical systems under periodic influences. The obtained results can be used in particular in further investigations of a non-trivial dynamics of hydromechanical systems, under working for the methods of a control of hydromechanical systems. |
| first_indexed | 2024-04-24T16:50:59Z |
| format | Article |
| id | doaj.art-be924d795c904b889a932bfc9ec02421 |
| institution | Directory Open Access Journal |
| issn | 0869-6632 2542-1905 |
| language | English |
| last_indexed | 2024-04-24T16:50:59Z |
| publishDate | 2024-03-01 |
| publisher | Saratov State University |
| record_format | Article |
| series | Известия высших учебных заведений: Прикладная нелинейная динамика |
| spelling | doaj.art-be924d795c904b889a932bfc9ec024212024-03-29T04:29:42ZengSaratov State UniversityИзвестия высших учебных заведений: Прикладная нелинейная динамика0869-66322542-19052024-03-0132219720810.18500/0869-6632-003091Peculiarities of the dynamics of a viscous liquid with a free boundary under periodic influencesSennitskii, Vladimir LeonidovichPurpose of the work is revealing and researching of peculiarities of a motion of a viscous liquid having a free boundary and undergoing periodic in time influences which are characterized by the absence of a predominant direction in space. Methods. The analytic investigation methods of non-linear problems, of boundary problems for the system of Navier– Stokes and continuity equations are used that are the method of perturbations (the method of a small parameter) the method of Fourier (the method of a separation of variables), an averaging, a construction and studying of asymptotic formulas. Results. A new problem on the motion of a viscous liquid is formulated and solved. Asymptotic representations of the found solution are constructed and explored. New hydromechanical effects are revealed. Conclusion. The work is fulfilled in the development of a perspective direction in liquid mechanics that is of researching the dynamics of hydromechanical systems under periodic influences. The obtained results can be used in particular in further investigations of a non-trivial dynamics of hydromechanical systems, under working for the methods of a control of hydromechanical systems.https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2024/03/and_2024-2_sennitskii_197-208.pdfviscous liquidfree boundaryperiodic in time influencespredominant direction in spacestationary motion |
| spellingShingle | Sennitskii, Vladimir Leonidovich Peculiarities of the dynamics of a viscous liquid with a free boundary under periodic influences Известия высших учебных заведений: Прикладная нелинейная динамика viscous liquid free boundary periodic in time influences predominant direction in space stationary motion |
| title | Peculiarities of the dynamics of a viscous liquid with a free boundary under periodic influences |
| title_full | Peculiarities of the dynamics of a viscous liquid with a free boundary under periodic influences |
| title_fullStr | Peculiarities of the dynamics of a viscous liquid with a free boundary under periodic influences |
| title_full_unstemmed | Peculiarities of the dynamics of a viscous liquid with a free boundary under periodic influences |
| title_short | Peculiarities of the dynamics of a viscous liquid with a free boundary under periodic influences |
| title_sort | peculiarities of the dynamics of a viscous liquid with a free boundary under periodic influences |
| topic | viscous liquid free boundary periodic in time influences predominant direction in space stationary motion |
| url | https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2024/03/and_2024-2_sennitskii_197-208.pdf |
| work_keys_str_mv | AT sennitskiivladimirleonidovich peculiaritiesofthedynamicsofaviscousliquidwithafreeboundaryunderperiodicinfluences |