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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2019, Volume 60, Issue 6, Pages 65–71
DOI: https://doi.org/10.15372/PMTF20190607 (Mi pmtf373) 		 
This article is cited in 15 scientific papers (total in 15 papers)

Exact solutions for the layered three-dimensional nonstationary isobaric flows of viscous incompressible fluid

N. M. Zubarevab, E. Yu. Prosviryakovc

a Institute of Electrophysics, Ural Branch, Russian Academy of Sciences, Ekaterinburg, 620016, Russia
b Lebedev Physical Institute, Russian Academy of Science, Moscow, 119991, Russia
c Institute of Engineering Science, Ural Branch, Russian Academy of Sciences, Ekaterinburg, 620016, Russia
Full-text PDF (203 kB) Citations (15)
DOI: https://doi.org/10.15372/PMTF20190607
Abstract: This paper describes an overdetermined system of equations that describes three-dimensional layered unsteady flows of a viscous incompressible fluid at a constant pressure. Studying the compatibility of this system makes it possible to reduce it to coupled quasilinear parabolic equations for velocity components. The reduced equations allow constructing several classes of exact solutions. In particular, polynomial and spatially localized self-similar solutions of the motion equations are obtained. The passage to the limit of the case of an ideal fluid is investigated.
Keywords: layered flows, isobaric flows, exact solutions, overdetermined system of equations, compatibility conditions.
Funding agency Grant number
Ural Branch of the Russian Academy of Sciences 18-1-1-5
18-2-2-15
Russian Foundation for Basic Research 17-08-00430
Russian Academy of Sciences - Federal Agency for Scientific Organizations 2
Received: 05.03.2019
Revised: 20.05.2019
Accepted: 27.05.2019
English version:
Journal of Applied Mechanics and Technical Physics, 2019, Volume 60, Issue 6, Pages 1031–1037
DOI: https://doi.org/10.1134/S0021894419060075
Bibliographic databases:
Document Type: Article
UDC: 532.5
Language: Russian
Citation: N. M. Zubarev, E. Yu. Prosviryakov, “Exact solutions for the layered three-dimensional nonstationary isobaric flows of viscous incompressible fluid”, Prikl. Mekh. Tekh. Fiz., 60:6 (2019), 65–71; J. Appl. Mech. Tech. Phys., 60:6 (2019), 1031–1037
Citation in format AMSBIB
\Bibitem{ZubPro19}
\by N.~M.~Zubarev, E.~Yu.~Prosviryakov
\paper Exact solutions for the layered three-dimensional nonstationary isobaric flows of viscous incompressible fluid
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2019
\vol 60
\issue 6
\pages 65--71
\mathnet{http://mi.mathnet.ru/pmtf373}
\crossref{https://doi.org/10.15372/PMTF20190607}
\elib{https://elibrary.ru/item.asp?id=41444464}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2019
\vol 60
\issue 6
\pages 1031--1037
\crossref{https://doi.org/10.1134/S0021894419060075}
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Prikladnaya Mekhanika i Tekhnicheskaya Fizika Prikladnaya Mekhanika i Tekhnicheskaya Fizika
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