Geodesic
Hydrodynamic Theory of Sound Wave Propagation
Teoretičeskaâ i matematičeskaâ fizika, Tome 129 (2001) no. 1, pp. 140-152
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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 $10^{-12}$sec${}^{-1}$, 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. 
@article{TMF_2001_129_1_a12,
     author = {G. A. Martynov},
     title = {Hydrodynamic {Theory} of {Sound} {Wave} {Propagation}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {140--152},
     year = {2001},
     volume = {129},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_129_1_a12/}
}
TY  - JOUR
AU  - G. A. Martynov
TI  - Hydrodynamic Theory of Sound Wave Propagation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2001
SP  - 140
EP  - 152
VL  - 129
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2001_129_1_a12/
LA  - ru
ID  - TMF_2001_129_1_a12
ER  - 
%0 Journal Article
%A G. A. Martynov
%T Hydrodynamic Theory of Sound Wave Propagation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2001
%P 140-152
%V 129
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2001_129_1_a12/
%G ru
%F TMF_2001_129_1_a12
G. A. Martynov. Hydrodynamic Theory of Sound Wave Propagation. Teoretičeskaâ i matematičeskaâ fizika, Tome 129 (2001) no. 1, pp. 140-152. http://geodesic.mathdoc.fr/item/TMF_2001_129_1_a12/

[1] L. D. Landau, E. M. Lifshits, Mekhanika sploshnykh sred, Gostekhizdat, M., 1954 | MR

[2] C. Truesdell, J. Rat. Mech. Analys., 2 (1953), 643 | MR | Zbl

[3] D. Sette, “Izuchenie prostykh zhidkostei ultrazvukovymi metodami”, Fizika prostykh zhidkostei, eds. G. Temperli, Dzh. Roulinson, Dzh. Rashbruk, Mir, M., 1973, 151

[4] Dzh. Ulenbek, Dzh. Ford, Lektsii po statisticheskoi mekhanike, Mir, M., 1965

[5] G. A. Martynov, UFN, 166:10 (1996), 1105 | DOI

[6] L. D. Landau, E. M. Lifshits, Statisticheskaya fizika, Chast 1, Nauka, M., 1976 | MR

[7] S. Chepmen, T. Kauling, Matematicheskaya teoriya neodnorodnykh gazov, Inostrannaya literatura, M., 1960 | MR

[8] Yu. L. Klimontovich, Statisticheskaya teoriya otkrytykh sistem, T. 1, Yanus, M., 1995