Bibliography

1

A.I. Dyachenko, A.O. Korotkevich, V.E. Zakharov, Weak turbulence of gravity waves, JETP Letters, 77, No. 10, 2003; Phys. Rev. Lett., 92, 13, 134501 (2004).

2

M. Onorato et.al., Freely decaying weak turbulence for sea surface gravity waves, Phys.Review L 89 No.14, September 2002.

3

N. Yokoyama, Statistics of Gravity Waves obtained by direct numerical simulation, JFM 501, 169-178 (2004).

4

Y. Choi, Y.V. Lvov, S. Nazarenko,B. Pokorni, Anomalous probability of large amplitudes in wave turbulence, Physics Letters A, 339, Issue 3-5, p. 361-369 (also on arXiv:math-ph/0404022 v1 & Apr 2004).

5

Y. Choi, Y.V. Lvov, S. Nazarenko, Probability Densities and Preservation of Randomness in Wave Turbulence Physics Letters A, 332, 230-238 (2004); Joint statistics of amplitudes and phases in wave turbulence, Physica D 201 (2005) 121-149; Y.Choi, Y.V. Lvov, S. Nazarenko; Wave turbulence, in "Recent developments in fluid dynamics" 5 (2004), Transworld Research Network, Kepala, India (also on arXiv.org:math-ph/0412045).

6

Y. Lvov and S. Nazarenko, "Noisy" spectra, long correlations and intermittency in wave turbulence, Phys. Rev. E 69, 066608 (2004)

7

K. Hasselmann, J. Fluid Mech 12 481 (1962).

8

V.E.Zakharov and Filonenko, J. Appl. Mech. Tech. Phys. 4 506-515 (1967).

9

A.C. Newell, V.E. Zakharov, Rough sea foam, PRL 69 No.8, August 1992.

10

L. Biven, S.V. Nazarenko and A.C. Newell, ''Breakdown of wave turbulence and the onset of intermittency'' Phys Lett A, 280, 28-32, (2001). A.C. Newell, S.V. Nazarenko and L. Biven, Physica D, 152-153, 520-550, (2001).

11

S. Nazarenko, ``Sandpile behaviour in discrete water-wave turbulence'', J. Stat. Mech. (2006) L02002 doi:10.1088/1742-5468/2006/02/L02002 (arXiv: nlin.CD/0510054).

12

Peter A.E.M. Janssen, Nonlinear four-wave interactions and freak waves, Journal of Phys.Oceanography, 33, April 2003.

13

V.I. Shrira, D.V. Ivonin, P. Broche and J.C. Maistre, On remote sensing of vertical sheer of ocean surface currents by means of a single-frequency VHF radar, Geophys. Res. Lett, 28, p 3955 (2001).

14

A.N. Pushkarev, On the Kolmogorov and frozen turbulence in numerical simulation of capillary waves, Eur. J. Mech. B/Fluids 18, 345-352 (1999)

15

Choi, W. Nonlinear evolution equations for two-dimensional surface waves in a fluid of finite depth. J. Fluid Mech. 295, 381-394, (1995).

16

V.E. Zakharov, V.S. L'vov and G.Falkovich, "Kolmogorov Spectra of Turbulence", Springer-Verlag, 1992.

17

V.E. Zakharov, Stability of periodic waves of finite amplitude on surface of deep water, PMFT, No 2 (1968) 86-94.

18

V.E. Zakharov, Inverse and direct cascade in the wind-driven surface wave turbulence and wave-breaking, Proceedings of IUTAM Meeting on Wave Breaking (Sydney, 1991).

19

V.E. Zakharov, Weakly nonlinear waves on the surface of an ideal fluid, AMS Transl. 182, 1998.

20

A.N. Pushkarev, D. Resio, V.E. Zakharov, Weak turbulent approach to the wind-generated gravity sea waves, Physica D 184 (1-4) 29-63 (2003).

21

V. P. Krasitskii, On reduced equations in the Hamiltonian theory of weakly nonlinear surface-waves, J. Fluid Mech. 272, (1994) 1.

22

B. Rumpf and L. Biven, Weak turbulence and collapses in the Majda-Mc-Laughlin-Tabak equation: Fluxes in wavenumber and in amplitude space. Physica D 204 (2005), 188-203 (also on oai:arXiv.org:nlin/0503005 ).

23

E.A. Kartashova, On properties of weakly nonlinear wave interactions in resonators Physica D 54 (1-2): 125-134 Dec 1991; E.A. Kartashova, Weakly nonlinear theory of finite-size effects in resonators Phys.Rev.Lett 72 (13) 2013-2016, Mar 28, 1994; E. Kartashova, Wave resonances in systems with discrete spectra, AMS Transl. (2) 182, 1998.

24

A.I. Dyachenko, Y.V. Lvov, V.E. Zakharov, Five-wave interaction on the surface of deep fluid, Physica D 87 (1-4) 233-261 (1995).

25

Kartashova, Private Communications, 2006.

26

O. M. Phillips, On the dynamics of unsteady gravity waves of finite amplitude. 1. The elementary interactions J. Fluid Mech. 9 (1960) 193.

27

A.I. Dyachenko and V.E. Zakharov, Is free surface hydrodynamics an integrable system?, Physics Letters A 190 (2) (1994) 144-148.

28

C.Connaughton, S.Nazarenko, A. Pushkarev, Discreteness and quasiresonances in weak turbulence of capillary waves, Physical Review E, 63, 046306, (2001).

29

M.Tanaka, N.Yokoyama, Effects of discretization of the spectrum in water-wave turbulence, Fluid Dynamics Research 34 (2004) 199-216.

30

V.E. Zakharov, A.O. Korotkevich, A.N. Pushkarev and A.I. Dyachenko, Mesoscopic wave turbulence, 82, 8, 487-491 (2005).

31

S.N. Papakostas, Ch. Tsitouras, High phase-lag-order Runge-Kutta and Nystrom pairs, SIAM J.Sci.Comput. 21 No2, 1999.

32

V.E.Zakharov Statistical theory of gravity and capillar y waves on the surface of a finite-depth fluid, Eur.J.Mech. B/Fluids, 1999.

33

A.I.Dyachenko, Y.V.Lvov On the Hasselmann and Zakharov approaches to the kinetic equation for gravity waves, J.Phys.Oceanography, 2 5, No.12, December 1995.

34

M.V. Berry and M.R. Dennis, Phase singularities in isotropic random waves, Proc. Roy. Soc A 456 2059-2079 (2000).