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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2004, Volume 45, Issue 2, Pages 28–39 (Mi pmtf2355)  
This article is cited in 4 scientific papers (total in 4 papers)

Spatial stationary long waves in shear flows

V. M. Teshukov

Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090
Full-text PDF (244 kB) Citations (4)
Abstract: The system of integrodifferential equations describing the spatial stationary free-boundary shear flows of an ideal fluid in the shallow-water approximation is considered. The generalized characteristics of the model are found and the hyperbolicity conditions are formulated. A new class of exact solutions of the governing equations is obtained which is characterized by a special dependence of the desired functions on the vertical coordinate. The system of equations describing this class of solutions in the hyperbolic case is reduced to Riemann invariants. New exact solutions of the equations of motion are found.
Keywords: nonlinear waves, shallow water, rotational flow.
Received: 15.12.2003
English version:
Journal of Applied Mechanics and Technical Physics, 2004, Volume 45, Issue 2, Pages 172–180
DOI: https://doi.org/10.1023/B:JAMT.0000017579.43526.c2
Bibliographic databases:
Document Type: Article
UDC: 532.592.2; 517.958
Language: Russian
Citation: V. M. Teshukov, “Spatial stationary long waves in shear flows”, Prikl. Mekh. Tekh. Fiz., 45:2 (2004), 28–39; J. Appl. Mech. Tech. Phys., 45:2 (2004), 172–180
Citation in format AMSBIB
\Bibitem{Tes04}
\by V.~M.~Teshukov
\paper Spatial stationary long waves in shear flows
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2004
\vol 45
\issue 2
\pages 28--39
\mathnet{http://mi.mathnet.ru/pmtf2355}
\elib{https://elibrary.ru/item.asp?id=17249153}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2004
\vol 45
\issue 2
\pages 172--180
\crossref{https://doi.org/10.1023/B:JAMT.0000017579.43526.c2}
Linking options:
  • https://www.mathnet.ru/eng/pmtf2355
  • https://www.mathnet.ru/eng/pmtf/v45/i2/p28
    • This publication is cited in the following 4 articles:
    1. Yurii N. Grigoriev, Nail H. Ibragimov, Vladimir F. Kovalev, Sergey V. Meleshko, Lecture Notes in Physics, 806, Symmetries of Integro-Differential Equations, 2010, 57  crossref
    2. A. K. Khe, “Strong discontinuities in spatial stationary long-wave flows of an ideal incompressible fluid”, J. Appl. Mech. Tech. Phys., 50:2 (2009), 199–206  mathnet  mathnet  crossref
    3. A. A. Chesnokov, “Symmetries and exact solutions of the shallow water equations for a two-dimensional shear flow”, J. Appl. Mech. Tech. Phys., 49:5 (2008), 737–748  mathnet  mathnet  crossref
    4. V. M. Teshukov, A. K. Khe, “Model of a strong discontinuity for the equations of spatial long waves propagating in a free-boundary shear flow”, J. Appl. Mech. Tech. Phys., 49:4 (2008), 693–698  mathnet  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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