Soliton solutions and their spectrum in the theory of rolling waves

Authors

  • Demekhin E.A. Southern Scientific Center, Russian Academy of Science, Rostov-on-Don, Russian Federation
  • Kalaidin E.N. Kuban State University, Krasnodar, Russian Federation
  • Shapar E.M. Kuban State University, Krasnodar, Russian Federation

UDC

532.536

Abstract

The work considers the motion of rolling waves in inclined passages. This type of waves doesn’t depend on the boundary tension and may exist both in turbulent and laminar flow regimes. The set of Dressler’s hydraulic equations was generalized to describe the resistance of rolling waves to 3D disturbances, and their spectra have been developed. It has been established that positive rolling waves are resistant to 3D disturbances, while negative rolling waves are non-resistant.

Author info

  • Evgeniy A. Demekhin

    д-р физ.-мат. наук, заведующий лабораторией Южного научного центра РАН

  • Evgeniy N. Kalaidin

    канд. физ.-мат. наук, заведующий кафедрой экономико-математических методов и моделей Кубанского государственного университета

  • Elena M. Shapar

    аспирантка факультета прикладной математики Кубанского государственного университета

References

  1. Dressler R.F. Mathematical solution of the problem of roll waves in inclined open channels // Comm. Pure Appl. Math. 1949. Vol. 2. P. 149-194.
  2. Ляпидевский В.Ю., Тешуков В.М. Математические модели распространения длинных волн в неоднородной жидкости. Новосибирск: СО РАН, 2000. 420 с.
  3. Демехин Е.А., Шкадов В.Я. О трехмерных нестационарных волнах в стекающей пленке жидкости // Изв. АН СССР. МЖГ. 1984. №5. С. 21-27.
  4. Chang H.-C., Demekhin E.A. Complex wave dynamics on thin films. Elsevier, 2002. 402 p.

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Issue

No. 1 (2005)

Pages

23-28

Section

Mechanics

Dates

Submitted

February 15, 2005

Accepted

February 26, 2005

Published

March 31, 2005

How to Cite

[1]
Demekhin, E.A., Kalaidin, E.N., Shapar, E.M., Soliton solutions and their spectrum in the theory of rolling waves. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2005, № 1, pp. 23–28.

License

Copyright (c) 2005 Демёхин Е.А., Калайдин Е.Н., Шапарь Е.М.

Creative Commons License

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

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