S. Y. Annenkov and V. I. Shrira, Direct numerical simulation of evolution of random water wave fields: direct and inverse cascades, Proceedings of International Symposium Topical Problems of Nonlinear Wave Physics, St. Peterburg-Nizhny Novgorod, pp.2-9, 2005.

S. Y. Annenkov and V. I. Shrira, Direct numerical simulation of the statistical characteristics of wave ensembles, Doklady Russ, Acad. Sciences, vol.396, pp.1-4, 2004.

A. N. Babanin and Y. P. Soloviev, Field Investigation of Transformation of the Wind Wave Frequency Spectrum with Fetch and the Stage of Development, Journal of Physical Oceanography, vol.28, issue.4, pp.563-576, 1998.
DOI : 10.1175/1520-0485(1998)028<0563:FIOTOT>2.0.CO;2

S. Badulin, A. N. Pushkarev, D. Resio, and V. Zakharov, Direct and inverse cascade of energy, momentum and wave action in wind-driven sea, 7th International workshop on wave hindcasting and forecasting, pp.92-103, 2002.

S. I. Badulin, V. I. Shrira, C. Kharif, and M. Ioualalen, On two approaches to the problem of instability of short-crested water waves, Journal of Fluid Mechanics, vol.9, issue.-1, pp.297-325, 1995.
DOI : 10.1143/JPSJ.53.3788

A. M. Balk and V. E. Zakharov, Stability of weak-turbulent Kolmogorov spectra, Amer, Math. Soc. Transl. Ser, vol.2, issue.182, pp.31-81, 1998.

A. M. Balk and V. E. Zakharov, Stability of weakly turbulent Kolmogorov spectra, Sov. Phys. Dokl, vol.33, pp.270-272, 1988.

G. I. Barrenblatt, Scaling, self-similarity, and intermediate asymptotics: Dimensional analysis and intermediate asymptotics, 1979.
DOI : 10.1017/CBO9781107050242

J. A. Battjes, T. J. Zitman, and L. H. Holthuijsen, A Reanalysis of the Spectra Observed in JONSWAP, Journal of Physical Oceanography, vol.17, issue.8, pp.1288-1295, 1987.
DOI : 10.1175/1520-0485(1987)017<1288:AROTSO>2.0.CO;2

M. Benoit, Evaluation of methods to compute the non-linear quadruplet interactions for deep-water wave spectra, Proc. 5th Int. Symp. on Ocean Wave Measurement and Analysis (WAVES'2005) Paper 52, 2005.

N. Booij, R. C. Ris, and L. H. Holthuijsen, A third-generation wave model for coastal regions, Part I, Model description and validation, J. Geoph. Res, vol.4, issue.104, pp.7649-7666, 1999.

M. A. Donelan, J. Hamilton, H. , and W. H. , Directional Spectra of Wind-Generated Waves, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.315, issue.1534, pp.509-562, 1985.
DOI : 10.1098/rsta.1985.0054

M. A. Donelan and W. J. Pierson-jr, Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry, Journal of Geophysical Research, vol.9, issue.C2, pp.4971-5029, 1987.
DOI : 10.1029/JC092iC05p04971

A. I. Dyachenko, A. O. Korotkevich, and V. E. Zakharov, Weak Turbulent Kolmogorov Spectrum for Surface Gravity Waves, Physical Review Letters, vol.92, issue.13, pp.134501-134502, 2004.
DOI : 10.1103/PhysRevLett.92.134501

R. Glazman, Surface gravity waves at equilibrium with a steady wind, Journal of Geophysical Research, vol.19, issue.4, pp.5249-5262, 1994.
DOI : 10.1029/93JC03317

T. Hara and S. E. Belcher, Wind forcing in the equilibrium range of wind-wave spectra, Journal of Fluid Mechanics, vol.470, pp.223-245, 2002.
DOI : 10.1017/S0022112002001945

N. Hashimoto, I. J. Haagsma, and L. H. Holthuijsen, Fourwave interactions in SWAN, Proc. 28th Int. Conf. Coastal Engng, 2003.

K. Hasselmann, On the non-linear energy transfer in a gravity-wave spectrum Part 1. General theory, Journal of Fluid Mechanics, vol.7, issue.04, pp.481-500, 1962.
DOI : 10.1017/S0022112062000373

K. Hasselmann, On the non-linear energy transfer in a gravity wave spectrum Part 2. Conservation theorems; wave-particle analogy; irrevesibility, Journal of Fluid Mechanics, vol.12, issue.02, pp.273-281, 1963.
DOI : 10.1017/S0022112063000239

K. Hasselmann, On the spectral dissipation of ocean waves due to white capping, Boundary Layer Met, pp.107-127, 1974.

K. Hasselmann, T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright et al., Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project, Dtsch. Hydrogh, p.8, 1973.

S. Hasselmann, K. Hasselmann, J. H. Allender, and T. P. Barnett, Computations and Parameterizations of the Nonlinear Energy Transfer in a Gravity-Wave Specturm. Part II: Parameterizations of the Nonlinear Energy Transfer for Application in Wave Models, Journal of Physical Oceanography, vol.15, issue.11, pp.1378-1391, 1985.
DOI : 10.1175/1520-0485(1985)015<1378:CAPOTN>2.0.CO;2

S. Hasselmann and K. Hasselmann, A symmetrical method of computing the nonlinear transfer in a gravity wave spectrum Hamburger Geophysikalische Einzelschriften, 1981.

S. Hasselmann and K. Hasselmann, Computations and Parameterizations of the Nonlinear Energy Transfer in a Gravity-Wave Spectrum. Part I: A New Method for Efficient Computations of the Exact Nonlinear Transfer Integral, Journal of Physical Oceanography, vol.15, issue.11, pp.1369-1377, 1985.
DOI : 10.1175/1520-0485(1985)015<1369:CAPOTN>2.0.CO;2

S. V. Hsiao and O. H. Shemdin, Measurements of wind velocity and pressure with a wave follower during Marsen, Journal of Geophysical Research: Oceans, vol.10, issue.C14, pp.14-9841, 1983.
DOI : 10.1029/JC088iC14p09841

R. Iroshnikov, Possibility of formation of a nonisotropic spectrum of wind waves by their weak nonlinear interaction, Soviet Physics Doklady, pp.1321-1325, 1986.

P. A. Janssen, Nonlinear Four-Wave Interactions and Freak Waves, Journal of Physical Oceanography, vol.33, issue.4, pp.863-884, 2003.
DOI : 10.1175/1520-0485(2003)33<863:NFIAFW>2.0.CO;2

K. K. Kahma, A Study of the Growth of the Wave Spectrum with Fetch, Journal of Physical Oceanography, vol.11, issue.11, pp.1505-1515, 1981.
DOI : 10.1175/1520-0485(1981)011<1503:ASOTGO>2.0.CO;2

A. V. Katz and V. M. Kontorovich, Drift stationary solutions in the weak turbulence theory, JETP Lett, vol.14, pp.265-267, 1971.

A. V. Katz and V. M. Kontorovich, Anisotropic turbulent distributions for waves with a non-decay dispersion law, Soviet Physics JETP, vol.38, pp.102-107, 1974.

A. V. Katz, V. M. Kontorovich, S. S. Moiseev, and N. V. , Power-like solutions of the kinetic Boltzmann equation for distributions of particles with spectral fluxes, JETP Lett, vol.21, pp.5-6, 1975.

A. V. Kats, V. M. Kantorovich, S. S. Moiseev, and V. Novikov, Exact power law solutions of the particle kinetic equations, Soviet Physics JETP, vol.44, pp.93-103, 1976.

S. A. Kitaigorodskii, Applications of the theory of similarity to the analysis of wind-generated wave motion as a stochastic process, Bull. Acad. Sci. USSR, Geophys. Ser., Engl. Transl, vol.1, pp.105-117, 1962.

V. P. Krasitskii, On reduced equations in the Hamiltonian theory of weakly nonlinear surface waves, Journal of Fluid Mechanics, vol.71, issue.-1, pp.1-20, 1994.
DOI : 10.1017/S0022112085002488

R. H. Kraichnan, Inertial Ranges in Two-Dimensional Turbulence, Physics of Fluids, vol.10, issue.7, pp.1417-1423, 1967.
DOI : 10.1063/1.1762301

K. Komatsu and A. Masuda, A new scheme of nonlinear energy transfer among wind waves: RIAM method-algorithm and performance-, Journal of Oceanography, vol.17, issue.Heft 3, pp.509-537, 1996.
DOI : 10.1007/BF02239052

G. J. Komen, S. Hasselmann, and K. Hasselmann, On the Existence of a Fully Developed Wind-Sea Spectrum, Journal of Physical Oceanography, vol.14, issue.8, pp.1271-1285, 1984.
DOI : 10.1175/1520-0485(1984)014<1271:OTEOAF>2.0.CO;2

G. J. Komen, L. Cavaleri, M. Donelan, K. Hasselmann, S. Hasselmann et al., Dynamics and modelling of ocean waves, 1995.
DOI : 10.1017/CBO9780511628955

I. V. Lavrenov, Wind waves in ocean, Physics and numerical simulation, 2003.

I. Lavrenov, D. Resio, and V. Zakharov, Numerical simulation of weak turbulent Kolmogorov spectrum in water surface waves, 7th International workshop on wave hindcasting and forecasting, pp.104-116, 2002.

O. Lavrova and . Yu, On transversal instability of finite depth water waves, Izv. Atm. Ocean. Phys, vol.19, pp.1068-1074, 1983.

M. S. Longuet-higgins, Parasitic capillary waves: a direct calculation, Journal of Fluid Mechanics, vol.230, issue.-1, pp.79-107, 1995.
DOI : 10.1175/1520-0485(1985)015 2.0.CO;2

M. S. Longuet-higgins, Progress towards understanding how waves break, The 21st Symposium on Naval Hydrodynamics, pp.7-28, 1996.

A. Masuda, Nonlinear Energy Transfer Between Wind Waves, Journal of Physical Oceanography, vol.10, issue.12, pp.2082-2092, 1980.
DOI : 10.1175/1520-0485(1980)010<2082:NETBWW>2.0.CO;2

A. Masuda, O. M. Phillips, and K. Hasselmann, Nonlinear Energy Transfer between Random Gravity Waves, pp.136-149, 1986.
DOI : 10.1007/978-1-4684-8980-4_3

W. K. Melville, The Role of Surface-Wave Breaking in Air-Sea Interaction, Annual Review of Fluid Mechanics, vol.28, issue.1, pp.279-321, 1996.
DOI : 10.1146/annurev.fl.28.010196.001431

L. W. Nordheim, On the Kinetic Method in the New Statistics and Its Application in the Electron Theory of Conductivity, Proc. Roy. Soc. London, A, pp.689-698, 1928.
DOI : 10.1098/rspa.1928.0126

M. Onorato, A. Osborne, M. Serio, D. Resio, A. Pushkarev et al., Freely Decaying Weak Turbulence for Sea Surface Gravity Waves, Physical Review Letters, vol.89, issue.14, pp.1-3, 2002.
DOI : 10.1103/PhysRevLett.89.144501

M. Onorato, A. Osborne, M. Serio, and C. L. , Quasi- Resonant Interactions and Non-gaussian statistics in long crested waves, Proceedings of Rogue waves, pp.20-22, 2004.

M. Onorato, A. Osborne, and M. Serio, On deviations from Guassian statistics for surface gravity waves, 14th 'Aha Huliko'a Winter Workshop ROGUE WAVES, pp.24-28, 2005.

O. M. Phillips, The equilibrium range in the spectrum of wind-generated waves, Journal of Fluid Mechanics, vol.none, issue.04, pp.426-434, 1958.
DOI : 10.1007/BF02277929

O. M. Phillips, On the dynamics of unsteady gravity waves of finite amplitude Part 1. The elementary interactions, Journal of Fluid Mechanics, vol.8, issue.02, pp.193-217, 1960.
DOI : 10.1017/S0022112060001043

O. M. Phillips, Spectral and statistical properties of the equilibrium range in wind-generated gravity waves, Journal of Fluid Mechanics, vol.123, issue.-1, pp.505-531, 1985.
DOI : 10.1175/1520-0485(1980)010 2.0.CO;2

W. J. Pierson and L. A. Moskowitz, A proposed spectral form for fully developed wind seas based on the similarity theory of S. A. Kitaigorodskii, Journal of Geophysical Research, vol.69, issue.24, pp.5181-5190, 1964.
DOI : 10.1029/JZ069i024p05181

W. J. Plant, A relationship between wind stress and wave slope, Journal of Geophysical Research, vol.3, issue.C3, pp.3-1961, 1982.
DOI : 10.1029/JC087iC03p01961

V. G. Polnikov, Numerical Solution of the kinetic equation for surface gravity waves, Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana, vol.26, issue.2, pp.168-176, 1990.

V. G. Polnikov, Numerical Modeling of the formation of flux spectra for surface gravity waves, Izv. Akad. Nauk, Fiz. Atmos. Okeana, vol.29, issue.6, pp.837-841, 1993.

A. N. Pushkarev, D. Resio, and V. E. Zakharov, Second generation diffusion model of interacting gravity waves on the surface of deep fluid, Nonlinear Processes in Geophysics, vol.11, issue.3, pp.329-342, 2004.
DOI : 10.5194/npg-11-329-2004
URL : https://hal.archives-ouvertes.fr/hal-00302341

A. N. Pushkarev, D. Resio, and V. E. Zakharov, Weak turbulent approach to the wind-generated gravity sea waves, Physica D: Nonlinear Phenomena, vol.184, issue.1-4, pp.29-63, 2003.
DOI : 10.1016/S0167-2789(03)00212-4

D. T. Resio and W. A. Perrie, Equilibrium Range for Wind-Generated Waves, Journal of Physical Oceanography, vol.19, issue.2, pp.193-204, 1989.
DOI : 10.1175/1520-0485(1989)019<0193:IOAERF>2.0.CO;2

D. Resio and W. Perrie, A numerical study of nonlinear energy fluxes due to wave-wave interactions Part 1. Methodology and basic results, Journal of Fluid Mechanics, vol.113, issue.-1, pp.603-629, 1991.
DOI : 10.1175/1520-0485(1989)019 2.0.CO;2

R. L. Snyder, F. W. Dobson, J. A. Elliot, and R. B. Long, Array measurements of atmospheric pressure fluctuations above surface gravity waves, Journal of Fluid Mechanics, vol.32, issue.-1, pp.1-59, 1981.
DOI : 10.1017/S0022112062001160

R. W. Stewart, The air-sea momentum exchange, Boundary-Layer Meteorology, pp.151-167, 1974.

J. H. Rasmussen and M. Stiassnie, Discretization of Zakharov's equation, European Journal of Mechanics - B/Fluids, vol.18, issue.3, pp.151-167, 1999.
DOI : 10.1016/S0997-7546(99)80033-8

M. Tanaka, A method of studying nonlinear random field of surface gravity waves by direct numerical simulation, Fluid Dynamics Research, vol.28, issue.1, pp.41-60, 2000.
DOI : 10.1016/S0169-5983(00)00011-3

Y. Toba, Local balance in the air-sea boundary processes, Journal of the Oceanographical Society of Japan, vol.29, issue.5, pp.209-220, 1973.
DOI : 10.1007/BF02108528

Y. Toba and W. Perrie, Wind-wave strong wave interactions and quasi-local equilibrium between wind and wind sea with the friction velocity proportionality Advances in Fluid Mechanics, Nonlinear ocean waves, pp.1-59, 1997.

H. J. Tolman, Effects of Numerics on the Physics in a Third-Generation Wind-Wave Model, Journal of Physical Oceanography, vol.22, issue.10, pp.1095-1111, 1992.
DOI : 10.1175/1520-0485(1992)022<1095:EONOTP>2.0.CO;2

H. L. Tolman and D. Chalikov, Source Terms in a Third-Generation Wind Wave Model, Journal of Physical Oceanography, vol.26, issue.11, pp.2497-2518, 1996.
DOI : 10.1175/1520-0485(1996)026<2497:STIATG>2.0.CO;2

B. Tracy and D. T. Resio, Theory and calculation of the nonlinear energy transfer between sea waves in deep water, WES Rep, 1982.

D. J. Webb, Non-linear transfers between sea waves, Deep-Sea Res, pp.279-298, 1978.

I. R. Young, Wind Generated Ocean Waves, p.306, 1999.

V. E. Zakharov, Problems of the theory of nonlinear surface waves, Budker Institute for Nuclear Physics, 1966.

V. E. Zakharov, Stability of periodic waves of finite amplitude on the surface of a deep fluid, Journal of Applied Mechanics and Technical Physics, vol.10, issue.no. 4, pp.86-94, 1968.
DOI : 10.1007/BF00913182

V. E. Zakharov, Statistical theory of gravity and capillary waves on the surface of a finite-depth fluid, European Journal of Mechanics - B/Fluids, vol.18, issue.3, pp.327-344, 1999.
DOI : 10.1016/S0997-7546(99)80031-4

V. E. Zakharov, Theoretical interpretation of fetch limited winddriven sea observations, 7th International workshop on wave hindcasting and forecasting, pp.86-92, 2002.

V. E. Zakharov, Direct and inverse cascades in the wind-driven sea, AGU Geophysical Monograph, pp.1-9, 2005.

V. E. Zakharov and N. N. Filonenko, Energy spectrum for stochastic oscillations of the surface of a fluid, Dokl. Acad. Nauk USSR, vol.160, pp.1292-1295, 1966.

V. E. Zakharov and M. M. Zaslavsky, The kinetic equation and Kolmogorov spectra in the weak-turbulence theory of wind waves, Izv. Atm. Ocean. Phys, vol.18, pp.747-753, 1982.

V. E. Zakharov and M. M. Zaslavsky, Dependence of wave parameters on the wind velocity, duration of its action and fetch in the weak-turbulence theory of water waves, Izv. Atm. Ocean. Physics, vol.19, pp.300-306, 1983.

V. E. Zakharov and A. N. Pushkarev, Diffusion model of interacting gravity waves on the surface of deep fluid, Nonlinear Processes in Geophysics, vol.6, issue.1, pp.1-10, 1999.
DOI : 10.5194/npg-6-1-1999
URL : https://hal.archives-ouvertes.fr/hal-00301922