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

José Marín Antuña


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.


Rotating fluid; helicoidal movement; rotating axis; acoustic oscillations


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.



  • There are currently no refbacks.

Copyright (c) 2015 Nova Scientia

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.


Nova Scientia is a multidisciplinary, electronic publication that publishes twice a year in the months of May and November; it is published by the Universidad De La Salle Bajío and aims to distribute unpublished and original papers from the different scientific disciplines written by national and international researchers and academics. It does not publish reviews, bibliographical revisions, or professional applications.

Nova Scientia, year 12, issue 24, May – October 2020, is a biannual journal printed by the Universidad De La Salle Bajío, with its address: Av. Universidad 602, Col. Lomas del Campestre, C. P. 37150, León, Gto. México. Phone: (52) 477 214 3900, Chief editor: Ph.D. Ramiro Rico Martínez. ISSN 2007 - 0705. Copyright for exclusive use No. 04-2008-092518225500/102, Diffusion rights via computer net 04 - 2008 – 121011584800-203 both granted by the Instituto Nacional del Derecho de Autor.

Editor responsible for updating this issue: Direction of Research Department of the Universidad De La Salle Bajío, last updated on May 15th, 2020.