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Teoreticheskaya i Matematicheskaya Fizika, 2001, Volume 129, Number 1, Pages 140–152
DOI: https://doi.org/10.4213/tmf526
(Mi tmf526)
 

This article is cited in 7 scientific papers (total in 7 papers)

Hydrodynamic Theory of Sound Wave Propagation

G. A. Martynov

Institute of Physical Chemistry, Russian Academy of Sciences
Full-text PDF (223 kB) Citations (7)
References:
Abstract: We formulate the limits of applicability of the hydrodynamic equations and prove the necessity of introducing a correction to the potential energy transfer in the heat conductivity equation, which allows developing the hydrodynamic theory of the propagation of sound waves with small amplitudes. We show that this correction affects almost all predictions of the standard hydrodynamic theory. In particular, this correction allows extending the applicability domain of the hydrodynamic theory to the case of an arbitrarily viscous liquid. Moreover, in total accordance with the experimental data, the theory predicts that the sound speed and the damping rate remain finite at all frequencies up to frequencies of the order of 1012sec1, while the hydrodynamic equations make no sense at higher frequencies and sound wave propagation in the medium consequently becomes impossible. We show that the dimensionless dispersion equation contains only one material parameter. We predict the existence of the highly damped second sound.
Received: 22.12.2000
Revised: 12.02.2001
English version:
Theoretical and Mathematical Physics, 2001, Volume 129, Issue 1, Pages 1428–1438
DOI: https://doi.org/10.1023/A:1012479814017
Bibliographic databases:
Language: Russian
Citation: G. A. Martynov, “Hydrodynamic Theory of Sound Wave Propagation”, TMF, 129:1 (2001), 140–152; Theoret. and Math. Phys., 129:1 (2001), 1428–1438
Citation in format AMSBIB
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\by G.~A.~Martynov
\paper Hydrodynamic Theory of Sound Wave Propagation
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\pages 140--152
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\crossref{https://doi.org/10.4213/tmf526}
\zmath{https://zbmath.org/?q=an:1113.76449}
\transl
\jour Theoret. and Math. Phys.
\yr 2001
\vol 129
\issue 1
\pages 1428--1438
\crossref{https://doi.org/10.1023/A:1012479814017}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000172400800013}
Linking options:
  • https://www.mathnet.ru/eng/tmf526
  • https://doi.org/10.4213/tmf526
  • https://www.mathnet.ru/eng/tmf/v129/i1/p140
  • This publication is cited in the following 7 articles:
    1. Martynov G.A., “Fluctuation theory of critical phenomena in fluids”, Russ. J. Phys. Chem. A, 90:7 (2016), 1338–1349  crossref  isi  elib  scopus
    2. Maximov G.A., “Generalized Variational Principle for Dissipative Continuum Mechanics”, Mechanics of Generalized Continua - One Hundred Years After the Cosserats, Advances in Mechanics and Mathematics, 21, 2010, 297–305  crossref  mathscinet  isi
    3. Maximov G.A., “A Generalized Variational Principle for Dissipative Hydrodynamics and its Application to Biot's Theory for the Description of a Fluid Shear Relaxation”, Acta Acustica united with Acustica, 96:2 (2010), 199–207  crossref  isi  elib  scopus  scopus
    4. Kobryn, AE, “Statistical-mechanical theory of ultrasonic absorption in molecular liquids”, Journal of Chemical Physics, 126:4 (2007), 044504  crossref  adsnasa  isi  scopus  scopus
    5. G. A. Martynov, “General Theory of Acoustic Wave Propagation in Liquids and Gases”, Theoret. and Math. Phys., 146:2 (2006), 285–294  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. Maksimov G.A., “On the variational principle in dissipative hydrodynamics”, Proceedings of the International Conference Days on Diffraction 2006, 2006, 173–177  crossref  isi  scopus  scopus
    7. G. A. Martynov, “Thermodynamics and Hydrodynamics (Statistical Foundations): 3. Hydrodynamic Equations”, Theoret. and Math. Phys., 134:3 (2003), 427–438  mathnet  crossref  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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