1932

Abstract

We overview the wave turbulence approach by example of one physical system: gravity waves on the surface of an infinitely deep fluid. In the theoretical part of our review, we derive the nonlinear Hamiltonian equations governing the water-wave system and describe the premises of the weak wave turbulence theory. We outline derivation of the wave-kinetic equation and the equation for the probability density function, and most important solutions to these equations, including the Kolmogorov-Zakharov spectra corresponding to a direct and an inverse turbulent cascades, as well as solutions for non-Gaussian wave fields corresponding to intermittency. We also discuss strong wave turbulence as well as coherent structures and their interaction with random waves. We describe numerical and laboratory experiments, and field observations of gravity wave turbulence, and compare their results with theoretical predictions.

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2016-03-10
2024-06-13
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Literature Cited

  1. Zakharov VE, Lvov VS, Falkovich GG. 1.  1992. Kolmogorov Spectra of Turbulence Berlin: Springer-Verlag [Google Scholar]
  2. Nazarenko S. 2.  2011. Wave Turbulence. Heidelberg: Springer [Google Scholar]
  3. Zakharov VE. 3.  1968. J. Appl. Mech. Tech. Phys. 9:2190–94 [Google Scholar]
  4. Krasitskii VP. 4.  1994. J. Fluid Mech. 272:1–20 [Google Scholar]
  5. Zakharov V. 5.  1999. Eur. J. Mech. B 18:327–44 [Google Scholar]
  6. Eyink GL, Shi YK. 6.  2012. Phys. D: Nonlinear Phenom. 241:1487–511 [Google Scholar]
  7. Choi Y, Lvov YV, Nazarenko S. 7.  2005. Phys. D: Nonlinear Phenom. 201:121–49 [Google Scholar]
  8. Hasselmann K. 8.  1962. J. Fluid Mech. 12:481–500 [Google Scholar]
  9. Zakharov VE. 9.  1965. J. Appl. Mech. Tech. Phys. 6:422–24 [Google Scholar]
  10. Zakharov VE, Zaslavskii M. 10.  1982. Izv. Acad. Nauk SSSR, Atmos. Ocean Phys. 18:970 [Google Scholar]
  11. Goldreich P, Sridhar S. 11.  1995. Astrophys. J. 438:763–75 [Google Scholar]
  12. Nazarenko SV, Schekochihin AA. 12.  2011. J. Fluid Mech. 677:134–53 [Google Scholar]
  13. Phillips OM. 13.  1958. J. Fluid Mech. 4:426–34 [Google Scholar]
  14. Kadomtsev BB. 14.  1965. Plasma Turbulence New York: Academic [Google Scholar]
  15. Kuznetsov EA. 15.  2004. J. Exp. Theor. Phys. Lett. 80:83–89 [Google Scholar]
  16. Nazarenko S, Lukaschuk S, McLelland S, Denissenko P. 16.  2010. J. Fluid Mech. 642:395–420 [Google Scholar]
  17. Onorato M, Osborne A, Serio M, Resio D, Pushkarev A. 17.  et al. 2002. Phys. Rev. Lett. 89:144501 [Google Scholar]
  18. Yokoyama N. 18.  2004. J. Fluid Mech. 501:169–78 [Google Scholar]
  19. Lvov YV, Nazarenko S, Pokorni B. 19.  2006. Phys. D: Nonlinear Phenom. 218:24–35 [Google Scholar]
  20. Zakharov VE, Korotkevich AO, Pushkarev A, Dyachenko A. 20.  2005. J. Exp. Theor. Phys. Lett. 82:487–91 [Google Scholar]
  21. Nazarenko S. 21.  2006. J. Stat. Mech.: Theory Exp. 2006:L02002 [Google Scholar]
  22. Kartashova E, Nazarenko S, Rudenko O. 22.  2008. Phys. Rev. E 78:016304 [Google Scholar]
  23. Denissenko P, Lukaschuk S, Nazarenko S. 23.  2007. Phys. Rev. Lett. 99:014501 [Google Scholar]
  24. L'vov V, Nazarenko S. 24.  2010. Phys. Rev. E 82:056322 [Google Scholar]
  25. Dyachenko A, Korotkevich A, Zakharov V. 25.  2003. J. Exp. Theor. Phys. Lett. 77:546–50 [Google Scholar]
  26. Choi Y, Lvov YV, Nazarenko S, Pokorni B. 26.  2005. Phys. Lett. A 339:361–69 [Google Scholar]
  27. Dyachenko AI, Korotkevich AO, Zakharov VE. 27.  2004. Phys. Rev. Lett. 92:134501 [Google Scholar]
  28. Korotkevich AO. 28.  2008. Phys. Rev. Lett. 101:074504 [Google Scholar]
  29. Annenkov SY, Shrira VI. 29.  2006. Phys. Rev. Lett. 96:204501 [Google Scholar]
  30. Shrira VI, Annenkov SY. 30.  2013. World Sci. Ser. Nonlinear Sci 83:239–81 [Google Scholar]
  31. Badulin SI, Pushkarev AN, Resio D, Zakharov VE. 31.  2005. Nonlinear Process. Geophys. 12:891–945 [Google Scholar]
  32. Badulin SI, Babanin AV, Zakharov VE, Resio D. 32.  2007. J. Fluid Mech. 591:339–78 [Google Scholar]
  33. Gagnaire-Renou E, Benoit M, Badulin SI. 33.  2011. J. Fluid Mech. 669:178–213 [Google Scholar]
  34. Miles JW. 34.  1957. J. Fluid Mech. 3:185–204 [Google Scholar]
  35. Donelan MA, Hamilton J, Hui WH. 35.  1985. Philos. Trans. R. Soc. Lond. A: Math. Phys. Eng. Sci. 315:509–62 [Google Scholar]
  36. Hwang PA, Wang DW, Walsh EJ, Krabill WB, Swift RN. 36.  2000. J. Phys. Oceanogr. 30:2753–67 [Google Scholar]
  37. Romero L, Melville WK. 37.  2010. J. Phys. Oceanogr. 40:441–65 [Google Scholar]
  38. Toba Y. 38.  1973. J. Oceanogr. Soc. Jpn. 29:209–20 [Google Scholar]
  39. Falcón C, Falcon E, Bortolozzo U, Fauve S. 39.  2009. Europhys. Lett. 86:14002 [Google Scholar]
  40. Lukaschuk S, Nazarenko S, McLelland S, Denissenko P. 40.  2009. Phys. Rev. Lett. 103:044501 [Google Scholar]
  41. Mukto MA, Atmane MA, Loewen MR. 41.  2007. Exp. Fluids 42:131–42 [Google Scholar]
  42. Falcon E, Laroche C, Fauve S. 42.  2007. Phys. Rev. Lett. 98:094503 [Google Scholar]
  43. Herbert E, Mordant N, Falcon E. 43.  2010. Phys. Rev. Lett. 105:144502 [Google Scholar]
  44. Falcon E. 44.  2010. Discret. Contin. Dyn. Syst. Ser. B 13:819–40 [Google Scholar]
  45. Deike L, Miquel B, Gutiérrez-Matus P, Jamin T, Semin B. 45.  et al. 2015. J. Fluid Mech. 781:196–225 [Google Scholar]
  46. Issenmann B, Falcon E. 46.  2013. Phys. Rev. E 87:011001 [Google Scholar]
  47. Deike L, Laroche C, Falcon E. 47.  2011. Europhys. Lett. 96:34004 [Google Scholar]
  48. Cobelli P, Maurel A, Pagneux V, Petitjeans P. 48.  2009. Exp. Fluids 46:1037–47 [Google Scholar]
  49. Faraday M. 49.  1831. Philos. Trans. R. Soc. Lond. 121:299–318 [Google Scholar]
  50. Gallagher I, Saint-Raymond L, Texier B. 50.  2013. From Newton to Boltzmann: Hard spheres and short-range potentials Zurich Lect. Adv. Math., Eur. Math. Soc. [Google Scholar]
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