Periodic surface disturbances in the concentration-stratified viscous fluid

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Abstract

The propagation of two-dimensional periodic capillary-gravitational periodic disturbances of a free surface in a viscous uniformly stratified liquid is investigated. Dispersion relations describing periodic surface flows of physical quantities are obtained. It is shown that there are additional flow components that are absent in the model of an ideal fluid. The obtained dispersion relations uniformly converge to the known expressions in the limit transitions.

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About the authors

A. A. Ochirov

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

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

References

  1. Ландау Л.Д., Лифшиц Е.М. Курс теоретической физики. Т. 6. Гидродинамика. М.: Наука, 1986. 736 с.
  2. Уизем Дж. Линейные и нелинейные волны. М.: Мир, 1977. 638 с; Whitham G.B. Linear and nonlinear waves. N. Y.: Wiley-Interscience, 1999.
  3. Лэмб Г. Гидродинамика. М.-Л.: ГИТТЛ, 1949. 928 с.
  4. Longuet-Higgins M.S. // Phil. Trans. Royal. Soc. London. Ser. A. 1953. No. 245. P. 535.
  5. Сретенский Л.Н. // Труды ЦАГИ. 1941. № 541. С. 1.
  6. Калиниченко В.А. // Прикл. матем. и мех. 2022. Т. 86. № 3. С. 370.
  7. Chashechkin Yu.D., Ilinykh A.Yu. // Axioms. 2023. V. 12. No. 4. P. 374.
  8. Huang F., Meng Q., Cao L. et al. // Ocean Eng. 2022. V. 250. Art No. 111062.
  9. Zheng M.M., Liu Y.D., Tang Y.Y. et al. // Ocean Eng. 2022. V. 263. Art No. 112366.
  10. Aleebrahim M.A., Jamali M. // Phys. Fluids. 2022. V. 34. No. 3. Art. No. 036602.
  11. Ильиных А.Ю., Чашечкин Ю.Д. // Изв. РАН. Мех. жидкости и газа. 2023. № 1. С. 54; Il’inykh A.Yu., Chashechkin Yu.D. // Fluid Dynamics. 2023. V. 58. No. 1. P. 31.
  12. Ильиных А.Ю. // Прикл. матем. и мех. 2019. Т. 83. № 3. С. 413; Ilʼinykh A.Yu. // Fluid Dynam. 2019. V. 83. No. 3. P. 927.
  13. Очиров А.А., Чашечкин Ю.Д. // Изв. РАН. Физ. атмосф. и океана. 2022. Т. 58. № 5. С. 524; Ochirov А.А., Chashechkin Yu.D. // Izv. Atmosph. Oceanic Phys. 2022. V. 58. No. 5. P. 450.
  14. Чашечкин Ю.Д., Очиров А.А., Лапшина К.Ю. // Физ-хим. кинетика в газовой динамике. 2022. Т. 23. № 6. doi: 10.33257/PhChGD.23.6.1028.
  15. Очиров А.А. // Изв. РАН. Сер. физ. 2023. Т. 87. № 1. С. 94; Ochirov A.A. // Bull. Russ. Acad. Sci. Phys. 2023. V. 87. No. 1. P. 79.
  16. Chashechkin Yu.D., Ochirov A.A. // Axioms. 2022. V. 11. No. 8. P. 1.
  17. Chashechkin Yu.D. // Axioms. 2021. V. 10. No. 4. P. 286.
  18. Найфэ А. Введение в методы возмущений. М.: Мир, 1984. 535 с.; Nayfeh A.H. Introduction to perturbation technique. N. Y.: John Wiley & Sons, 1993.
  19. Кикоин И.К. Таблицы физических величин. Справочник. М.: Атомиздат, 1976. 1008 с.

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2. Fig. 1. Dependence of the linear scale of the current components on the frequency of periodic motion of (a) wavelength, (b) velocity field ligament, (c) salinity ligament.

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3. Fig. 2. Dependence of the phase (dashed lines) and group (solid lines) velocity on the frequency of periodic motion of (a) wavelength, (b) velocity field ligament, (c) salinity ligament.

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4. Fig. 3. Dependence of phase (dashed lines) and group (solid lines) velocity on (a) wavelength, (b) velocity field ligament, (c) salinity ligament.

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