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Issue 2, 2026
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60th anniversary of the L.D. Landau Institute for Theoretical Physics RAS. Reviews of topical problems


Nonlinear generation of currents by waves on liquid surface

†  a, b, ‡  c, §  a, b
a Landau Institute for Theoretical Physics, Russian Academy of Sciences, prosp. Akademika Semenova 1A, Chernogolovka, Moscow Region, 142432, Russian Federation
b HSE University, ul. Myasnitskaya 20, Moscow, 101000, Russian Federation
c Osipyan Institute of Solid State Physics, Russian Academy of Sciences, Akademika Osip'yana str. 2, Chernogolovka, Moscow Region, 142432, Russian Federation

Attenuation of surface waves due to viscous dissipation is accompanied by the excitation of slow vortex currents due to the conservation of total momentum. We present a theoretical model for small-amplitude waves that explains experiments on vortex flow generation by crossing waves. Special attention is paid to the effect of surface contaminants, which is accounted for within the framework of a model of a thin elastic liquid film, leading to enhanced wave dissipation and intensified vortex currents. As the amplitude of the currents increases, their interaction with the waves must be considered. A theoretical framework is proposed to describe this interaction, demonstrating its applicability to classical problems: Guyon waves, the propagation of short waves against a current, and Langmuir circulation. Finally, experimental data on the turbulent regime of flow generation, which occurs at sufficiently large wave amplitudes, are described, and open questions in this field are outlined.

Fulltext pdf (1.1 MB)
Fulltext is also available at DOI: 10.3367/UFNe.2025.08.039992
Keywords: waves on liquid surface, surface film, vortex flow, mass current, Stokes drift, virtual wave stress, vortex force, wave scattering and refraction
PACS: 05.45.−a, 92.10.hb (all)
DOI: 10.3367/UFNe.2025.08.039992
URL: https://ufn.ru/en/articles/2025/11/f/
2-s2.0-105027277871
2025PhyU...68.1131V
Citation: Vergeles S S, Levchenko A A, Parfenyev V M "Nonlinear generation of currents by waves on liquid surface" Phys. Usp. 68 1131–1150 (2025)
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Received: 30th, March 2025, revised: 3rd, August 2025, 5th, August 2025

Оригинал: Вергелес С С, Левченко А А, Парфеньев В М «Нелинейная генерация течений волнами на поверхности жидкости» УФН 195 1199–1220 (2025); DOI: 10.3367/UFNr.2025.08.039992

References (109) ↓ Cited by (1) Similar articles (1)

  1. Stokes G G Trans. Cambridge Philos. Soc. 8 441 (1847)
  2. Longuet-Higgins M S Philos. Trans. R. Soc. A 245 535 (1953)
  3. Longuet-Higgins M S Proc. R. Soc. London A 311 371 (1969)
  4. Weber J E J. Geophys. Res. Oceans 106 11653 (2001)
  5. Stuart J T J. Fluid Mech. 24 673 (1966)
  6. Ünlüata U, Mei C C J. Geophys. Res. 75 7611 (1970)
  7. Dore B D Quart. J. Mech. Appl. Math. 30 157 (1977)
  8. Madsen O S J. Phys. Oceanogr. 8 1009 (1978)
  9. Weber J E J. Fluid Mech. 137 115 (1983)
  10. Xu Z, Bowen A J J. Phys. Oceanogr. 24 1850 (1994)
  11. Eeltink D et al Wave Motion 97 102610 (2020)
  12. Filatov S V et al Phys. Rev. Lett. 116 054501 (2016)
  13. Filatov S V, Aliev S A, Levchenko A A, Khramov D A JETP Lett. 104 702 (2016); Filatov S V, Aliev S A, Levchenko A A, Khramov D A Pis’ma Zh. Eksp. Teor. Fiz. 104 714 (2016)
  14. Francois N et al Nature Commun. 8 14325 (2017)
  15. Xia H et al Fluids 4 (2) 74 (2019)
  16. Abella A P, Soriano M N Phys. Scr. 95 085007 (2020)
  17. Filatov S V, Orlov A V, Brazhnikov M Yu, Levchenko A A JETP Lett. 108 519 (2018); Filatov S V, Orlov A V, Brazhnikov M Yu, Levchenko A A Pis’ma Zh. Eksp. Teor. Fiz. 108 549 (2018)
  18. Abella A P, Soriano M N J. Exp. Theor. Phys. 130 452 (2020); Abella A P, Soriano M N Zh. Eksp. Teor. Fiz. 157 539 (2020)
  19. Smirnova D A, Nori F, Bliokh K Y Phys. Rev. Lett. 132 054003 (2024)
  20. Wang B et al Nature 638 394 (2025)
  21. von Kameke A et al Phys. Rev. Lett. 107 074502 (2011)
  22. Francois N et al Phys. Rev. Lett. 110 194501 (2013)
  23. Francois N et al Phys. Rev. X 4 021021 (2014)
  24. Colombi R, Schlüter M, von Kameke A Exp. Fluids 62 8 (2021)
  25. Colombi R et al Fluids 7 (5) 148 (2022)
  26. Levich V G Zh. Eksp. Teor. Fiz. 10 1296 (1940)
  27. Levich V G Zh. Eksp. Teor. Fiz. 11 340 (1941)
  28. Levich V G Physicochemical Hydrodynamics (Englewood Cliffs, NJ: Prentice-Hall, 1962), translated from Russian 1st ed.; 3rd Russian ed., rev. and enlarged, Levich V G Fiziko-khimicheskaya Gidrodinamika (Moscow - Izhevsk: Inst. Komp’yut. Issled., 2016)
  29. Miles J W Proc. R. Soc. London A 297 459 (1967)
  30. Lucassen-Reynders E H, Lucassen J Adv. Colloid Interface Sci. 2 347 (1970)
  31. Henderson D M J. Fluid Mech. 365 89 (1998)
  32. Henderson D M, Segur H J. Geophys. Res. Oceans 118 5074 (2013)
  33. Campagne A et al Phys. Rev. Fluids 3 044801 (2018)
  34. Van Dorn W G J. Fluid Mech. 24 769 (1966)
  35. Parfenyev V M, Vergeles S S, Lebedev V V Phys. Rev. E 94 052801 (2016)
  36. Parfenyev V M, Vergeles S S Phys. Rev. Fluids 3 064702 (2018)
  37. Parfenyev V M et al Phys. Rev. Fluids 4 114701 (2019)
  38. Langevin D Annu. Rev. Fluid Mech. 46 47 (2014)
  39. Francois N et al Phys. Rev. E 92 023027 (2015)
  40. Parfenyev V M, Vergeles S S Phys. Rev. Fluids 5 094702 (2020)
  41. Filatov S V, Poplevin A V, Levchenko A A, Parfenyev V M Physica D 434 133218 (2022)
  42. Riley N Annu. Rev. Fluid Mech. 33 43 (2001)
  43. Lord Rayleigh Philos. Trans. R. Soc. London 175 1 (1884)
  44. Boluriaan S, Morris P Int. J. Aeroacoust. 2 255 (2003)
  45. Landau L D, Lifshitz E M Fluid Mechanics (Oxford: Pergamon Press, 1987); Translated from English, Landau L D, Lifshitz E M Gidrodinamika (Moscow: Fizmatlit, 2001)
  46. Subbotin S, Shiryaeva M Microgravity Sci. Technol. 34 89 (2022)
  47. Subbotin S et al Phys. Fluids 35 074110 (2023)
  48. Riley N IMA J. Appl. Math. 3 419 (1967)
  49. Lyubimova T P et al Microgravity Sci. Technol. 37 45 (2025)
  50. Parfenyev V M, Vergeles S S, Lebedev V V JETP Lett. 103 201 (2016); Parfenyev V M, Vergeles S S, Lebedev V V Pis’ma Zh. Eksp. Teor. Fiz. 103 220 (2016)
  51. Parfenyev V M, Vergeles S S, Lebedev V V JETP Lett. 104 287 (2016)
  52. Yablonskii S V, Kurbatov N M, Parfenyev V M Phys. Rev. E 95 012707 (2017)
  53. Filatov S V, Levchenko A A, Mezhov-Deglin L P JETP Lett. 111 549 (2020); Filatov S V, Levchenko A A, Mezhov-Deglin L P Pis’ma Zh. Eksp. Teor. Fiz. 111 653 (2020)
  54. Filatov S V, Khramov D A, Levchenko A A JETP Lett. 106 330 (2017); Filatov S V, Khramov D A, Levchenko A A Pis’ma Zh. Eksp. Teor. Fiz. 106 305 (2017)
  55. Boffetta G, Ecke R E Annu. Rev. Fluid Mech. 44 427 (2012)
  56. Craik A D D, Leibovich S J. Fluid Mech. 73 401 (1976)
  57. Holm D D Physica D 98 415 (1996)
  58. Vergeles S S, Vointsev I A Phys. Fluids 36 034119 (2024); Vergeles S S, Vointsev I A arXiv:2310.19533
  59. Abrashkin A A, Pelinovsky E N Phys. Usp. 65 453 (2022); Abrashkin A A, Pelinovsky E N Usp. Fiz. Nauk 192 491 (2022)
  60. Stewart R H, Joy J W Deep Sea Res. Oceanogr. Abstracts 21 1039 (1974)
  61. Andrews D G, McIntyre M J. Fluid Mech. 89 647 (1978)
  62. Fabrikant A L, Stepanyants Yu A Propagation Of Waves In Shear Flows (Singapore: World Scientific, 1998); Translated from Russian, Fabrikant A L, Stepanyants Yu A Rasprostranenie Voln V Sdvigovykh Potokakh (Moscow: Fizmatlit, 1996)
  63. Peregrine D H Adv. Appl. Mech. 16 9 (1976)
  64. Basovich A Ya, Talanov V I Izv. Akad. Nauk SSSR. Fiz. Atmos. Okeana 13 766 (1977)
  65. Craik A D D J. Fluid Mech. 81 209 (1977)
  66. Lamb H Hydrodynamics 6th ed. (Cambridge: Cambridge Univ. Press, 1975)
  67. Longuet-Higgins M S, Stewart R W J. Fluid Mech. 8 565 (1960)
  68. Longuet-Higgins M S, Stewart R Deep Sea Res. Oceanogr. Abstracts 11 529 (1964)
  69. van den Bremer T S, Breivik Ø Philos. Trans. R. Soc. A 376 20170104 (2018)
  70. Monismith S G J. Fluid Mech. 884 F1 (2020)
  71. van den Bremer T S et al J. Fluid Mech. 879 168 (2019)
  72. Calvert R et al Phys. Rev. Fluids 4 114801 (2019)
  73. Phillips O M The Dynamics Of The Upper Ocean (Cambridge: Cambridge Univ. Press, 1977); Translated into Russian, Phillips O M Dinamika Verkhnego Sloya Okeana (Leningrad: Gidrometeoizdat, 1980)
  74. Stepanyants Yu A, Fabrikant A L Sov. Phys. Usp. 32 783 (1989); Stepanyants Yu A, Fabrikant A L Usp. Fiz. Nauk 159 83 (1989)
  75. Dysthe K B Proc. R. Soc. London A 369 105 (1979)
  76. Longuet-Higgins M S J. Fluid Mech. 17 459 (1963)
  77. Lucassen J Trans. Faraday Soc. 64 2221 (1968)
  78. Rajan G K Int. J. Eng. Sci. 154 103340 (2020)
  79. Alpers W, Hühnerfuss H J. Geophys. Res. Oceans 94 6251 (1989)
  80. Ruvinsky K D, Feldstein F I, Freidman G I J. Fluid Mech. 230 339 (1991)
  81. Gershuni G Z, Lyubimov D V Thermal Vibrational Convection (Chichester: John Wiley and Sons, 1998)
  82. Belonozhko D F, Kozin A V Fluid Dyn. 46 270 (2011)
  83. Shmyrov A V et al J. Fluid Mech. 877 495 (2019)
  84. Whitham G B Linear And Nonlinear Waves (New York: Wiley, 1974); Translated into Russian, Whitham G B Lineinye I Nelineinye Volny (Moscow: Mir, 1977)
  85. Kamchatnov A M Teoriya Lineinykh I Nelineinykh Voln (Theory Of Linear And Nonlinear Waves) (Moscow: Izd. Dom Vysshei Shkoly Ekonomiki, 2025)
  86. Lee K, Mizutani N Int. J. Offshore Polar Eng. 17 259 (2007)
  87. Romero L, Lenain L, Melville W K J. Phys. Oceanogr. 47 615 (2017)
  88. Thorpe S A Annu. Rev. Fluid Mech. 36 55 (2004)
  89. Fox-Kemper B, Johnson L, Qiao F Ocean Mixing: Drivers, Mechanisms And Impacts (Eds M Meredith, A N Garabato) (Amsterdam: Elsevier, 2022) p. 65-94
  90. Samodurov A S et al Phys. Oceanogr. 30 689 (2023); Translated from Russian, Samodurov A S et al Morskoi Gidrofiz. Zh. 39 735 (2023)
  91. Leibovich S Annu. Rev. Fluid Mech. 15 391 (1983)
  92. Kawamura T J. Marine Sci. Technol. 5 161 (2000)
  93. Fujiwara Y, Yoshikawa Y J. Phys. Oceanogr. 50 2323 (2020)
  94. Veron F, Melville W K J. Fluid Mech. 446 25 (2001)
  95. Craik A D D J. Fluid Mech. 125 37 (1982)
  96. Leibovich S J. Fluid Mech. 79 715 (1977)
  97. Molenaar D, Clercx H J H, van Heijst G J F Physica D 196 329 (2004)
  98. Xia H, Shats M, Falkovich G Phys. Fluids 21 125101 (2009)
  99. Bardóczi L et al Phys. Rev. E 90 063103 (2014)
  100. Doludenko A N et al Phys. Fluids 33 011704 (2021)
  101. Ruth D J, Coletti F J. Fluid Mech. 1001 A46 (2024)
  102. Jamin T, Berhanu M, Falcon E Phys. Rev. Fluids 10 034608 (2025); Jamin T, Berhanu M, Falcon E arXiv:2401.17871
  103. Flores O, Riley J J, Horner-Devine A R J. Fluid Mech. 821 248 (2017)
  104. Gorce J-B et al Proc. Natl. Acad. Sci. USA 116 25424 (2019)
  105. Hong S-H et al Sci. Adv. 6 eaaz9386 (2020)
  106. Falkovich G J. Fluid Mech. 638 1 (2009)
  107. Dias F, Dyachenko A I, Zakharov V E Phys. Lett. A 372 1297 (2008)
  108. Kolokolov I V, Lebedev V V, Parfenyev V M Phys. Rev. E 109 035103 (2024)
  109. Shikanian A, Parfenyev V Phys. Fluids 37 095127 (2025)
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