BREAKING OF INTERNAL SOLITARY WAVES IN A THREE-LAYER FLUID OVER AN OBSTACLE

封面

如何引用文章

全文:

开放存取 开放存取
受限制的访问 ##reader.subscriptionAccessGranted##
受限制的访问 订阅存取

详细

A three-layer shallow water model in the Boussinesq approximation with allowance for nonlinearity, dispersion, and mixing is used to describe the propagation and breaking of large-amplitude internal waves interacting with uneven bottom topography. The proposed equations of motion are solved numerically by applying the Godunov method with additional inversion of an elliptic operator at each time step. Stationary solutions in the form of mode-1 solitary waves are constructed. Mixing processes induced by breaking internal solitary waves due to their interaction with a single or combined obstacle are modeled. It is shown that the numerical results are in good agreement with experimental data and direct numerical simulation.

作者简介

V. Liapidevskii

Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences

Email: liapid@hydro.nsc.ru
Novosibirsk, Russia

A. Chesnokov

Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences

Email: chesnokov@hydro.nsc.ru
Novosibirsk, Russia

参考

  1. Helfrich K. R., Melville W. K. Long nonlinear internal waves // Annu. Rev. Fluid Mech. 2006. V. 38. P. 395–425.
  2. Lamb K. G. Internal wave breaking and dissipation mechanisms on the continental slope/shelf // Annu. Rev. Fluid Mech. 2014. V. 46. P. 231–254.
  3. Boegman L., Stastna M. Sediment resuspension and transport by internal solitary waves // Annu. Rev. Fluid Mech. 2-19. V. 51. P. 129–154.
  4. Lamb K. G., Farmer D. Instabilities in an internal solitary-like wave on the Oregon Shelf // J. Phys. Oceanogr. 2011. V. 41. P. 67–87.
  5. Lien R.-C., Henyey F., Ma B., Yang Y. J. Large-amplitude internal solitary waves observed in the northern South China Sea: Properties and energetics // J. Phys. Oceanogr. 2014. V. 44. P. 1095–1115.
  6. Ляпидевский В. Ю., Новотрясов В. В., Храпченков Ф. Ф., Ярощук И. О. Внутренний волновой бор в шельфовой зоне моря // ПМТФ. 2017. Т. 58,№5. С. 60–71.
  7. Sveen J. K., Guo Y., Davies P.A., Grue J. On the breaking of internal solitary waves at a ridge // J. Fluid Mech. 2002. V. 469. P. 161–188.
  8. Fructus D., Carr M., Grue J., Jensen A., Davies P.A. Shear-induced breaking of large internal solitary waves // J. Fluid Mech. 2009. 620. P. 1–29.
  9. Carr M., Franklin J., King S. E., Davies P. A., Grue J., Dritschel D. G. The characteristics of billows generated by internal solitary waves // J. Fluid Mech. 2017. V. 812. P. 541–577.
  10. Carr M., King S. E., Dritschel D. G. Numerical simulation of shear induced instabilities in internal solitary waves // J. Fluid Mech. 2011. V. 683. P. 263–288.
  11. Zhu H.,Wang L., Avital E. J., Tang H.,Williams J. J. R. Numerical simulation of interaction between internal solitary waves and submerged ridges // Appl. Ocean Res. 2016. V. 58. P. 118–134.
  12. Baines P. G. Topographic effects in stratified flows. Cambridge Univ. Press, 1995.
  13. Vlasenko V., Hutter K. Numerical experiments on the breaking of solitary internal waves over a slope-shelf topography // J. Phys. Oceanogr. 2002. V. 32. P. 1779–1793.
  14. Aghsaee P., Boegman L., Lamb K. G. Breaking of shoaling internal solitary waves // J. Fluid Mech. 2010. V. 659. P. 289–317.
  15. Ляпидевский В. Ю., Храпченков Ф. Ф., Чесноков А. А., Ярощук И. О. Моделирование нестационарных гидрофизических процессов на шельфе Японского моря // Изв. РАН. МЖГ. 2022.№1. С. 57–68.
  16. Chen C. Y. An experimental study of stratified mixing caused by internal solitary waves in a two-layered fluid system over variable seabed topography // Ocean Eng. 2007. V. 34. P. 1995–2008.
  17. Chen C.Y., Hsu J.R.C., Cheng M.H., Chen C.W. Experiments on mixing and dissipation in internal solitary waves over two triangular obstacles // Environ. Fluid Mech. 2008. V. 8. P. 199–214.
  18. Mu H., Chen X., Li Q. Laboratory experiments on an internal solitary wave over a triangular barrier // J. Ocean Univ. China. 2019. V. 18. P. 1061–1069.
  19. Nian X., Zhang L., Sun X., Zhang E. Mechanism analysis of internal solitary waves breaking encountering submarine ridges based on laboratory experiments // AIP Adv. 2023. V. 13. 075110. P. 1–13.
  20. Deepwell D., Stastna M., Carr M., Davies P.A. Wave generation through the interaction of a mode-2 internal solitary wave and a broad, isolated ridge // Phys. Rev. Fluids. 2019. V. 4. 094802. P. 1–22.
  21. Choi W., Camassa R. Fully nonlinear internal waves in a two-fluid system // J. Fluid Mech. 1999. V. 396. P. 1–36.
  22. Barros R., Choi W., Milewski P. A. Strongly nonlinear effects on internal solitary waves in three-layer flows // J. Fluid Mech. 2020. V. 883. A16. P. 1–36.
  23. Ляпидевский В. Ю., Чесноков А. А. Слой смешения в двухслойных спутных течениях стратифицированной жидкости // ПМТФ. 2022. Т. 63,№6. С. 122–134.
  24. Ляпидевский В.Ю., Чесноков А. А. Равновесная модель слоя смешения в сдвиговом течении стратифицированной жидкости // ПМТФ. 2024. Т. 63,№3. С. 43–55.
  25. Chesnokov A., Shmakova N., Zhao B., Zhang T., Wang Z., Duan W. Large-amplitude internal waves and turbulent mixing in three-layer flows under a rigid lid // Phys. Fluids. 2024. V. 36. 072104. P. 1–15.
  26. Ляпидевский В. Ю. Математические модели распространения длинных волн в неоднородной жидкости / В.Ю. Ляпидевский, В. М. Тешуков. Новосибирск: Изд-во СО РАН, 2000.
  27. Chesnokov A. A., Liapidevskii V. Yu. Hyperbolic model of internal solitary waves in a three-layer stratified fluid // Europ. Phys. J. Plus. 2020. V. 135. 590. P. 1–19.
  28. Busto S., Dumbser M., Escalante C., Favrie N., Gavrilyuk S. On high order ADER discontinuous Galerkin schemes for first order hyperbolic reformulations of nonlinear dispersive systems // J. Sci. Comput. 2021. V. 87. 48. P. 1–47.
  29. Куликовский А.Г., Погорелов Н.В., Семенов А.Ю. Математические вопросы численного решения гиперболических систем уравнений. М.: Физматлит, 2001. 608 с.
  30. Nessyahu H., Tadmor E. Non-oscillatory central differencing schemes for hyperbolic conservation laws // J. Comput. Phys. 1990. V. 87. P. 408–463.

补充文件

附件文件
动作
1. JATS XML
下载

版权所有 © Russian Academy of Sciences, 2025