RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Trudy MIAN:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Tr. Mat. Inst. Steklova, 2013, Volume 281, Pages 188–198 (Mi tm3473)  
Classification of the types of instability of vertical flows in geothermal systems

A. T. Il'icheva, G. G. Tsypkinb

a Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia
b Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

Abstract: Stability of vertical flows in geothermal systems is investigated in the case when the domain occupied by water (heavy fluid) is located over the domain occupied by vapor. It is found that under the transition to an unstable regime in a neighborhood of the existing solution, a pair of new solutions appears as a result of the turning point bifurcation. We consider the dynamics of a narrow band of weakly unstable and weakly nonlinear perturbations of the plane surface of the water-to-vapor phase transition. It is shown that such perturbations obey the generalized Ginzburg–Landau–Kolmogorov–Petrovsky–Piscounov equation.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00335-a
11-01-12051-ofi-m
The work was supported by the Russian Foundation for Basic Research (project nos. 11-01-00335a and 11-01-12051-ofi-m-2011).


DOI: https://doi.org/10.1134/S0371968513020155

Full text: PDF file (206 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2013, 281, 179–188

Bibliographic databases:

Document Type: Article
UDC: 532.546
Received in September 2012

Citation: A. T. Il'ichev, G. G. Tsypkin, “Classification of the types of instability of vertical flows in geothermal systems”, Modern problems of mechanics, Collected papers. Dedicated to Academician Andrei Gennad'evich Kulikovskii on the occasion of his 80th birthday, Tr. Mat. Inst. Steklova, 281, MAIK Nauka/Interperiodica, Moscow, 2013, 188–198; Proc. Steklov Inst. Math., 281 (2013), 179–188

Citation in format AMSBIB
\Bibitem{IliTsy13}
\by A.~T.~Il'ichev, G.~G.~Tsypkin
\paper Classification of the types of instability of vertical flows in geothermal systems
\inbook Modern problems of mechanics
\bookinfo Collected papers. Dedicated to Academician Andrei Gennad'evich Kulikovskii on the occasion of his 80th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2013
\vol 281
\pages 188--198
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3473}
\crossref{https://doi.org/10.1134/S0371968513020155}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3479941}
\elib{http://elibrary.ru/item.asp?id=20193388}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2013
\vol 281
\pages 179--188
\crossref{https://doi.org/10.1134/S0081543813040159}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000322390600015}


Linking options:
  • http://mi.mathnet.ru/eng/tm3473
  • https://doi.org/10.1134/S0371968513020155
  • http://mi.mathnet.ru/eng/tm/v281/p188

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
    		• Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Number of views:
    This page:125
    Full text:8
    References:32
     
    Contact us:
    		  Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019