FREE SURFACE TWO-DIMENSIONAL PERIODIC DISTURBANCES IN VARIOUS MODELS OF THE FLUID

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription or Fee Access

Abstract

The complete dispersion relations of a flat free surface periodic perturbations with a positive definite frequency and a complex wavenumber taking into account spatial attenuation in a viscous stratified charged liquid were obtained in a linear approximation for the first time by methods of the theory of singular perturbations. Regular components of the complete solution describe plane gravitational-capillary waves. Singular components characterize ligaments – thin flows that are absent in the model of an ideal medium. The obtained dispersion relations in extreme cases uniformly transform into known expressions for inviscid stratified, viscous homogeneous and ideal liquids. The calculated dependencies of the wavelength and thickness of the ligament, the group and phase velocity of the components on the frequency at different values of the media parameters are given.

About the authors

Yu. D. Chashechkin

Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences

Author for correspondence.
Email: chakin@ipmnet.ru
Russia, Moscow

A. A. Ochirov

Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences

Author for correspondence.
Email: otchirov@mail.ru
Russia, Moscow

References

  1. Darrigol O. Worlds of flow. A history of hydrodynamics from the Bernoullis to Prandtl. Oxford. University Press. 2005. 356 p.
  2. Ландау Л.Д., Лифшиц Е.М. Курс теорет. физ. Т. 6. Гидродинамика. М.: Наука, 1986. 736 с.
  3. Уизем Дж. Линейные и нелинейные волны. М.: Мир, 1977. 638 с.
  4. Kistovich A.V., Chashechkin Yu.D. Propagating stationary surface potential waves in a deep ideal fluid // Water Resources. 2018. V. 45 № 5. P. 719–727. https://doi.org/10.1134/S0097807818050111
  5. Schlichting H. Boundary Layer Theory. N.Y.: McGraw Hill Co, 1955. 812 p.
  6. Longuet-Higgins M.S. Mass transport in the boundary layer at a free oscillating surface. // J. Fluid Mech. 1960. V. 8. № 2. P. 293–306. https://doi.org/10.1017/S002211206000061X
  7. Liu A., Davis S. Viscous attenuation of mean drift in water waves. // J. Fluid Mech. 1977. V. 81. № 1. P. 63–84. https://doi.org/10.1017/S0022112077001918
  8. Белоножко Д.Ф., Григорьев А.И. Нелинейные периодические волны на заряженной поверхности глубокой маловязкой электропроводной жидкости // Журнал технической физики. 2004. Т. 74. №. 3. С. 5–13.
  9. Федоров К.Н. Тонкая термохалинная структура вод Мирового океана. Л.: Гидрометеоиздат, 1976. 184 с.
  10. Chandrasekhar S. Hydrodynamic and hydromagnetic stability, International Series of Monographs on Physics. Oxford: Clarendon Press, 1961. 654 p.
  11. Лайтхилл Дж. Волны в жидкостях. M.: Мир, 1981. 598 с.
  12. Очиров А.А., Чашечкин Ю.Д. Двумерные периодические волны в невязкой непрерывно стратифицированной жидкости // Известия РАН. Физика атмосферы и океана. 2022. Т 58. № 5. С. 524–533. https://doi.org/10.31857/S000235152205008X
  13. Chashechkin Yu.D. Foundations of engineering mathematics applied for fluid flows // Axioms. 2021. V. 10. № 4. P. 286. https://doi.org/10.3390/axioms10040286
  14. Chashechkin Yu.D., Ochirov A.A. Periodic waves and ligaments on the surface of a viscous exponentially stratified fluid in a uniform gravity field // Axioms. 2022. V. 11. No. 8. P. 402. https://doi.org/10.3390/axioms11080402
  15. Nayfeh A., Hassan S. The method of multiple scales and non-linear dispersive waves // J. Fluid Mechanics. 1971. V. 48. № 3. P. 463–475.
  16. Найфэ А. Введение в методы возмущений М.: Мир, 1984. 535 с.
  17. Кистович А.В., Чашечкин Ю.Д. Отражение капиллярно-гравитационных волн от областей поверхностной конвекции // ДАН. 2005. Т. 404. № 2. С. 184–187.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download
2.

Download (29KB)
Indexing metadata
3.

Download (51KB)
Indexing metadata
4.

Download (59KB)
Indexing metadata
5.

Download (32KB)
Indexing metadata

Copyright (c) 2023 Ю.Д. Чашечкин, А.А. Очиров