Geodesic
Analysis of the Dispersion of Hydroacoustic Waves on the Basis of Viscoelastic Model
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 3, pp. 342-348.

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On the basis of mathematical model of the Poynting–Thomson viscoelastic medium the effect of acoustic dispersion of water is described: the phase velocity of waves of terahertz frequency is doubled in comparison with the velocity of waves of sound range. Rheological parameters of the model are selected by means of the values of the velocities of propagation of slow and fast monochromatic waves. The system of equations of the dynamics of the Poynting–Thomson viscoelastic medium is reduced to the form, hyperbolic by Friedrichs. It guarantees the correctness of the Cauchy problem and boundary value problems with dissipative boundary conditions, and also allows to use the monotone grid-characteristic schemes for numerical solution of problems. In the framework of 1D model the computations of a transformation of hydroacoustic waves, generated by $U$-shaped impulse of pressure, were performed. Results of computations show a strong damping of the fast precursor as it passes the distance of hundred nanometers from the moment of entry and the emergence of stable profile of the slow wave at the mesolevel.
Keywords: viscoelastic medium, Poynting–Thomson model, hydroacoustic wave, grid-characteristic method.
Mots-clés : dispersion 
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Vladimir M. Sadovskii; Oxana V. Sadovskaya; Kristina S. Svobodina. Analysis of the Dispersion of Hydroacoustic Waves  on the Basis of Viscoelastic Model. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 3, pp. 342-348. http://geodesic.mathdoc.fr/item/JSFU_2013_6_3_a7/

[1] G. Ruocco, F. Sette, “The history of the “fast sound” in liquid water”, Condensed Matter Physics, 11:1(53) (2008), 29–46 | DOI | MR

[2] S. C. Santucci, D. Fioretto, L. Comez, A. Gessini, C. Masciovecchio, Is there any fast sound in water?, Phys. Rev. Lett., 97:22 (2006), 225701-1–225701-4 | DOI

[3] O. Mishima, H. E. Stanley, “The relationship between liquid, supercooled and glassy water”, Nature, 396 (1998), 329–335 | DOI

[4] P. G. Debenedetti, H. E. Stanley, “Supercooled and glassy water”, Physics Today, 56:6 (2003), 40–46 | DOI

[5] P. A. Starodubtsev, R. N. Alifanov, S. V. Gutorova, “Modern methods for transmission of sound energy in water and their theoretical development”, Journal of Siberian Federal University. Mathematics and Physics, 2:2 (2009), 230–237 (in Russian)

[6] A. Rahman, F. H. Stillinger, “Propagation of sound in water. A molecular-dynamics study”, Phys. Rev. A, 10:1 (1974), 368–378 | DOI

[7] M. P. Allen, D. J. Tildesley, Computer Simulation of Liquids, Clarendon Press, Oxford, 1987 | Zbl

[8] M. Reiner, Deformation, Strain and Flow: an Elementary Introduction to Rheology, ed. H. K. Lewis, London, 1960 | MR

[9] O. Sadovskaya, V. Sadovskii, Mathematical Modeling in Mechanics of Granular Materials, Advanced Structured Materials, 21, Springer, Heidelberg–New York–Dordrecht–London, 2012 | DOI | Zbl

[10] K. O. Friedrichs, “Symmetric hyperbolic linear differential equations”, Commun. Pure Appl. Math., 7:2 (1954), 345–392 | DOI | MR | Zbl

[11] S. K. Godunov, Equations of Mathematical Physics, Nauka, M., 1979 (in Russian) | MR | Zbl