Two-layer equilibrium model of miscible inhomogeneous fluid flow

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详细

Two-layer flow of a density-stratified fluid with mass transfer between the layers is considered. In the Boussinesq approximation, the equations of motion are reduced to a homogeneous quasilinear system of partial differential equations of mixed type. The flow parameters in the intermediate mixed layer are determined from the equilibrium conditions in a more general model of three-layer flow of a miscible fluid. In particular, the equilibrium conditions imply the constancy of the interlayer Richardson number in velocity-shift flows. A self-similar solution to the problem of breakdown of an arbitrary discontinuity (the lock-exchange problem) in the domain of hyperbolicity of the system under consideration is constructed. The transcritical flow regimes over a local obstacle are studied and the conditions under which the obstacle determines the upstream flow are determined. A comparison of steady-state and time-dependent solutions with the solutions obtained for the original three-layer models of miscible fluid flow is carried out.

作者简介

V. Liapidevskii

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

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Email: liapid@hydro.nsc.ru
俄罗斯联邦, Novosibirsk

参考

  1. Helfrich K.R., Melville W.K. Long nonlinear internal waves // Ann. Rev. Fluid Mech. 2006. V. 38. P. 395–425. https://doi.org/10.1146/annurev.fluid.38.050304.092129
  2. Thorpe S.A., Li Lin. Turbulent hydraulic jumps in a stratified shear flow. Part 2 //J. Fluid Mech. 2014. V. 758. P. 94–120. https://doi.org/10.1017/jfm.2014.502
  3. Baines P.G. Internal hydraulic jumps in two-layer systems // J. Fluid Mech. 2016. V. 787. P. 1–15. https://doi.org/10.1017/jfm.2015.662
  4. Ogden K.A., Helfrich K.R. Internal hydraulic jumps in two-layer flows with increasing upstream shear // Phys. Rev. Fluids. 2020. V. 5. 074803. https://doi.org/10.1103/PhysRevFluids.5.074803
  5. Lawrence G.A., Armi L. Stationary internal hydraulic jumps // J. Fluid Mech. 2022. V. 936. A25. https://doi.org/10.1017/jfm.2022.74
  6. Rastello M., Hopfinger E.J. Sediment-entraining suspension clouds: a model of powder-snow avalanches // J. Fluid. Mech. 2004. V. 509. P. 181–206. https://doi.org/10.1017/S0022112004009322
  7. Ermanyuk E.V., Gavrilov N.V. A note on the propagation speed of a weakly dissipative gravity current // J. Fluid Mech. 2007. V. 574. P. 393–403. https://doi.org/10.1017/S0022112006004198
  8. Dai A. Experiments on gravity currents propagating on different bottom slopes // J. Fluid Mech. 2013. 731 pp. 117–141. https://doi.org/10.1017/jfm.2013.372
  9. Zhu R., He Z., Meiburg E. Mixing, entrainment and energetics of gravity currents released from two-layer stratified locks // J. Fluid Mech. 2023. V. 960. A1. https://doi.org/10.1017/jfm.2023.146
  10. Turner J.S. Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows // J. Fluid Mech. 1986. V. 183. P. 431–471. https://doi.org/10.1017/S0022112086001222
  11. Baines P.G. Topographic effects in stratified flows. Cambridge Univ. Press, 1995. 500 p. doi: 10.1017/9781108673983
  12. Klymak M., Moum J.N. Internal solitary waves of elevation advancing on a shoaling shelf // Geophys. Res. Lett. 2003. V. 30, Issue 20. 2045. https://doi.org/10.1029/2003GL017706
  13. Bourgault D., Kelley D.E., Galbraith P.S. Interfacial solitary wave run-up in the St. Lawrence Estuary // J. Marine Res. 2005. V. 63. P. 1001–1015. doi: 10.1357/002224005775247599
  14. Lamb K. Shoaling solitary internal waves: on a criterion for the formation of waves with trapped cores // J. Fluid Mech. 2003. V. 478. P. 81–100. https://doi.org/10.1017/S0022112002003269
  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. https://doi.org/10.31857/S0568528122010066
  16. Кириллов В.В., Ляпидевский В.Ю., Суторихин И.А., Храпченков. Ф.Ф. Особенности трансформации нелинейных внутренних волн на шельфе и в глубоком озере // Изв. РАН. МЖГ. 2023. № 6. С. 121–131. doi: 10.31857/S1024708423600537
  17. Parker G., Fukushima Y., Pantin H.M. Self-accelerating turbidity currents // J. Fluid Mech. 1986. V. 171. P. 145–81. https://doi.org/10.1017/S0022112086001404
  18. Liapidevskii V. Yu., Dutykh D. On the velocity of turbidity currents over moderate slopes // Fluid Dyn. Res. 2019. V. 51, № 3. 035501. doi: 10.1088/1873-7005/ab0091
  19. Уизем Дж. Линейные и нелинейные волны. Пер. с англ. М; Мир, 1977. 621 с.
  20. Ляпидевский В.Ю., Чесноков А.А. Равновесная модель слоя смешения в сдвиговом течении стратифицированной жидкости // ПМТФ. 2024. doi: 10.15372/PMTF202315412
  21. Ляпидевский В.Ю. Равновесная модель плотностного течения // Труды МИАН. 2023. Т. 322. № 6. С. 167–189. https://doi.org/10.4213/tm4303
  22. Ляпидевский В.Ю., Тешуков В.М. Математические модели распространения длинных волн в неоднородной жидкости. Изд-во СО РАН, Новосибирск, 2000, 420 с.
  23. Baines P.G. A unified description of two-layer flow over topography // J. Fluid Mech. 1984. V. 146. P. 127–167. https://doi.org/10.1017/S0022112084001798
  24. Lax P.D. Hyperbolic systems of conservation laws II// Comm. Pure Appl. Math. 1957. V. 10. P. 537–566. https://doi.org/10.1002/cpa.3160100406
  25. Рождественский Б.Л., Яненко Н.Н. Системы квазилинейных уравнений и их приложение к газовой динамике. М.: Наука, 1978. 687 c.
  26. Гаврилюк С.Л. Задача о распаде произвольного разрыва для газа Ван-дер-Ваальса // Динамика жидкости со свободными границами. Новосибирск: Ин-т гидродинамики СО АН СССР, 1985. С. 36–54. (Динамика сплошной среды; Вып. 69).
  27. Ляпидевский В.Ю. Течение Куэтта вязкоупругой среды максвелловского типа с двумя временами релаксации // Труды МИ АН. 2018, Т. 300. С. 146–157. doi: 10.1134/S0371968518010119
  28. Bukreev V.I, Gusev A.V., Liapidevskii V. Yu. Blocking effects in supercritical flows over topography // PIV and Modeling Water Wave Phenomena, Proc. of the Int. Symp. (Cambridge, UK, April 18–19, 2002), Univ. of Oslo (2002). P. 86–90.

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