Hydrodynamic Instability of Spatially Periodic Flows of Homogeneous and Stratified Fluid with Regard for Friction. Formation of Steady-State Vortex Disturbances

封面

如何引用文章

全文:

详细

The stability of spatially periodic flows of homogeneous and stratified fluid is investigated with regard for bottom friction. The Galerkin method with three basis Fourier harmonics is used to solve the stability problem. A system of ordinary differential equations for the amplitudes of the Fourier harmonics is formulated. A solution to the linearized version of the system is obtained and an expression for the increment of disturbance growth is found. It is established that at the nonlinear stage of development the exponential growth of linear disturbances is replaced by the regime of establishing steady-state periodic disturbances in form of closed cells. These disturbances reduce the averaged horizontal velocity of the flow. Analytical expressions for the spatial period and amplitude of steady-state disturbances are obtained.

作者简介

M. Kalashnik

Obukhov Institute of Atmospheric Physics of the Russian Academy of Sciences; Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences

Email: kalashnik-obn@mail.ru
Moscow, Russia

参考

  1. Булатов В.В., Владимиров Ю.В. Волны в стратифицированных средах. М.: Наука, 2015. 735 с.
  2. Гилл А. Динамика атмосферы и океана. М.: Мир, 1986. Т. 2. 415 с.
  3. Монин А.С. Теоретические основы геофизической гидродинамики. Л.: Гидрометеоиздат, 1988. 433 с.
  4. Обухов А.М. Течение Колмогорова и его лабораторное моделирование // УМН. 1983. Т. 38. Вып. 4 (232). С. 101–111.
  5. Гледзер Е.Б., Должанский Ф.В., Обухов А.М. Системы гидродинамического типа и их применение. М.: Наука. 1981. 366 с.
  6. Thess A. Instabilities in two-dimensional spatial periodic flows. Part I: Kolmogorov flow // Phys. Fluids A. 1992. V. 4 (7). P. 1385–1395.
  7. Мешалкин Л.Д., Синай Я.Г. Исследование устойчивости стационарного решения одной системы уравнений плоского движения несжимаемой вязкой жидкости // ПММ. 1961. Т. 25. № 6. С. 1700–1705.
  8. Goton K., Yamada M., Mizushima Y. The theory of stability of spatially periodic flows // J. Fluid Mech. 1983. V. 127. P. 45–58.
  9. Beaumont D. The stability of spatially periodic flows // J. Fluid Mech. 1981. V. 108. P. 461–474.
  10. Батчаев А.М., Курганский М.В. О неустойчивости периодического сдвигового течения слабостратифицированной жидкости // Известия AH CCCP. Физика атмосферы и океана. 1986. Т. 22. № 1. С. 3–9.
  11. Balmforth N.J, Young Y.N. Stratified Kolmogorov flow // J. Fluid Mech. 2002. V. 450. P. 131–167.
  12. Manfori A., Young W. Stability of β-plane Kolmogorov flow // Phys. D. 2002. V. 162. P. 208–232.
  13. Matsuda M. Stability of the basic solution of Kolmogorov flow with a bottom friction // Tokyo J. Math. 2010. V. 33. P. 65–72.
  14. Lucas D., Kerswell R. Spatiotemporal dynamics in two dimensional Kolmogorov flow over large domains // J. Fluid. Mech. 2014. V. 750. P. 518–554.
  15. Kim S., Okamoto H. Unimodal patterns appearing in the Kolmogorov flows at large Reynolds numbers // Nonlinearity. 2015. V. 28. P. 3219–3242.
  16. Sivashinsky G. Weak turbulence in periodic flows // Phys. D. 1985. No. 17. P. 243–255.
  17. Sivashinsky G., Yakhot V. Negative viscosity effect in large scale flows // Phys. Fluids. 1985. V. 28. P. 1040–1042.
  18. Kalashnik M., Kurgansky M. Nonlinear dynamics of long-wave perturbations of the Kolmogorov flow for large Reynolds numbers // Ocean Dyn. 2018. V. 68. P. 1001–1012.
  19. Boffetta G., Celani A., Mazzino A. Drag reduction in the turbulent Kolmogorov flow // Phys Rev. E. V. 71. 2005. 036307.
  20. Kalashnik M.V., Kurgansky M.V. Nonlinear Oscillations in a Two-Dimensional Spatially Periodic Flow // Eur. Phys. J. Plus. 2024. V. 139. No. 2. P. 1–11.
  21. Blumen W. Uniform potential vorticity flow: part I. Theory of wave interactions and two dimensional turbulence // J. Atmos. Sci. 1978. V. 35. P. 774–783.
  22. Held I.M., Pierrehumbert R.T., Garner S.T., Swanson K.L. Surface quasi-geostrophic dynamics // J. Fluid Mech. 1995. V. 282. P. 1–20.
  23. Pedlosky J. Geophysical Fluid Dynamics. Springer-Verlag. Berlin. New York. 1987. 710 p.
  24. Lapeyre G., Klein P. Dynamics of the upper oceanic layers in terms of surface quasigeostrophy theory // J. Phys. Oceanogr. 2006. V. 36. P. 165–176.
  25. Badin G. Surface semi-geostrophic dynamics in the ocean // J. Fluid Dyn. 2013. 107. P. 526–540.
  26. Harvey B., Ambaum M. Instability of surface temperature filaments in strain and shear // Quart. J. Roy. Meteor. Soc. 2010. V. 136. P. 1506–1513.
  27. Kalashnik M.V., Kurgansky M.V., Kostrykin S.V. Instability of surface quasigeostrophic spatially periodic flows // J. Atmos. Sci. 2020. V. 77. P. 239–255.
  28. Kalashnik M.V., Chkhetiani O.G., Kurgansky M.V. Discrete SQG models with two boundaries and baroclinic instability of jet flows // Phys. Fluids. 2021. V. 33. 076608.
  29. Калашник М.B., Курганский М.В., Чхетиани О.Г. Бароклинная неустойчивость в геофизической гидродинамике // УФН. 2022. Т. 192. № 10. С. 1110–1144.

补充文件

附件文件
动作
1. JATS XML
下载

版权所有 © Russian Academy of Sciences, 2025