An equation for waves in a fluid moving with rotating helical motion along the axis of rotation

Authors

  • José Marín Antuña Departamento de Física Teórica, Facultad de Física. Universidad de La Habana

DOI:

https://doi.org/10.21640/ns.v5i9.154

Keywords:

Rotating fluid, helicoidal movement, rotating axis, acoustic oscillations

Abstract

For possible applications in the theoretical study of wave processes in different kind of devices of important technical applications, and also from the pure physical and mathematical point of view, we develop a model to describe small acoustic oscillations in a rotating fluid with a helicoidal movement along the rotating axis. A non classical fourth order partial differential equation is obtained to describe such movements. We study some particular cases and compare this cases with equations obtained in previous papers.

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References

J.B. Morton and E.J. Shaughnessy, ``Waves in a gas in solid-body rotation'', J. Fluid Mech. (1972), 56, 2, 277-286.

John W. Miles,``Waves in a rapidly rotating gas'', J. Fluid Mech. (1981), 107, 487-497.

S.L. Soboliev, ``Sobre un nuevo problema de la Física Matemática (en ruso)'', Izv. AN SSSR serie matem.(1954)18, 1, 3-50.

V.N. Masliennikova, ``Problemas matemáticos de la hidrodinámica en un fluido rotatorio y sistemas de Soboliev (en ruso)'', Disertación de Doctor en Ciencias, Novosibirsk. (1971).

S.A. Gabov, ``Espectro y bases de autofunciones de un problema de oscilaciones acústicas en un fluido rotatorio (en ruso)'', Dokl. AN SSSR (1980), 254, 4, 777-779.

S.A. Gabov, J. Marín-Antuña, ``On a non-stationary problem for waves diffraction in a rotating compressible liquid'', Moscow University News, series 3, MSU, (1985), 26-3, 16-20.

J. Marín-Antuña, ``Ondas planas de amplitud variable en líquidos rotatorios compresibles. Problema de autovalores'', Rev. Cub. Fis. (1992), 12, 3, 214-219.

J. Marín-Antuña, ``Difraction of a step-like wave on a wall of longitude h in a compressible rotating fluid'', Rev. Cub. Fis. (2002), 19, 1, 23-25.

J. Marín-Antuña, R.L. Hall, N. Saad ``Wave equation and dispersion relations for a compressible rotating fluid'', Physics Letters A (2007), 362, 57 - 60

Y.D. Chashechkin. International Conference on Boundary and Interior Layers, BAIL 2004, Tolouse, France, July 2004.

K. Zhang, C.A. Jones, Geophys. Res. Lett. (1994) 24, 1939.

S.J. Friedlander, J. Geophys. J. R. Astron. Soc. (1987) 89, 637.

J.Marín-Antuña, A. Hernández-Rodríguez, O. Sotolongo Costa, ``An equation for waves in a viscous rotating compressible fluid'', in: Proc. DFD, APS, November 1995.

S.A. Gabov, A.G. Sveshnikov, A.K. Shatov, Dokl. Akad. Nauk SSSR (1983) 268, 1095.

L.M. Brekhovskikh, V. Goncharov, Mechanics of Continua and Wave Dynamics, second ed., Springer Series on Wave Phenomena, vol. 1, Springer- Verlag, New York, 1994.

G.B. Whitham, Linear and Nonlinear Waves, Wiley, New York, 1999.

S.A. Gabov. Nuevos Problemas de la Teoría de Ondas (en ruso), Moscú, Editorial Nauka, 1998.

L.D. Landau, E.M. Lifshitz, Fluid Mechanics, second ed., Pergamon Press, 1987.

L.D. Landau, E.M. Lifshitz, The Classical Theory of Fields. fourth revised ed., Pergamon Press, 1975.

Published

2014-10-28

How to Cite

Marín Antuña, J. (2014). An equation for waves in a fluid moving with rotating helical motion along the axis of rotation. Nova Scientia, 5(9), 19–28. https://doi.org/10.21640/ns.v5i9.154

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Natural Sciences and Engineering

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