Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 165
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Aijaz, Saima Rogers, W. Erick and Babanin, Alexander V. 2016. Wave spectral response to sudden changes in wind direction in finite-depth waters. Ocean Modelling, Vol. 103, p. 98.


    Humbert, T. Josserand, C. Touzé, C. and Cadot, O. 2016. Phenomenological model for predicting stationary and non-stationary spectra of wave turbulence in vibrating plates. Physica D: Nonlinear Phenomena, Vol. 316, p. 34.


    Jiang, Xingjie Wang, Daolong Gao, Dalu and Zhang, Tingting 2016. Experiments on exactly computing non-linear energy transfer rate in MASNUM-WAM. Chinese Journal of Oceanology and Limnology, Vol. 34, Issue. 4, p. 821.


    Kierkels, A. H. M. and Velázquez, J. J. L. 2016. On Self-Similar Solutions to a Kinetic Equation Arising in Weak Turbulence Theory for the Nonlinear Schrödinger Equation. Journal of Statistical Physics, Vol. 163, Issue. 6, p. 1350.


    Prabhakar, V. and Uma, G. 2016. A Polar Method using cubic spline approach for obtaining wave resonating quadruplets. Ocean Engineering, Vol. 111, p. 292.


    Pushkarev, Andrei and Zakharov, Vladimir 2016. Limited fetch revisited: Comparison of wind input terms, in surface wave modeling. Ocean Modelling, Vol. 103, p. 18.


    Rahman, Matiur 2016. Handbook of Fluid Dynamics, Second Edition.


    Sheremet, Alex Davis, Justin R. Tian, Miao Hanson, Jeffrey L. and Hathaway, Kent K. 2016. TRIADS: A phase-resolving model for nonlinear shoaling of directional wave spectra. Ocean Modelling, Vol. 99, p. 60.


    Uma, G. Prabhakar, V. and Hariharan, S. 2016. A wavelet approach for computing nonlinear wave–wave interactions in discrete spectral wave models. Journal of Ocean Engineering and Marine Energy, Vol. 2, Issue. 2, p. 129.


    Kierkels, A. H. M. and Velázquez, J. J. L. 2015. On the Transfer of Energy Towards Infinity in the Theory of Weak Turbulence for the Nonlinear Schrödinger Equation. Journal of Statistical Physics, Vol. 159, Issue. 3, p. 668.


    Nazarenko, Sergey 2015. Wave turbulence. Contemporary Physics, Vol. 56, Issue. 3, p. 359.


    Samiksha, S.V. Polnikov, V.G. Vethamony, P. Rashmi, R. Pogarskii, F. and Sudheesh, K. 2015. Verification of model wave heights with long-term moored buoy data: Application to wave field over the Indian Ocean. Ocean Engineering, Vol. 104, p. 469.


    Yildirim, B. and Karniadakis, George Em 2015. Stochastic simulations of ocean waves: An uncertainty quantification study. Ocean Modelling, Vol. 86, p. 15.


    Zhao, Xin Shen, Hayley H. and Cheng, Sukun 2015. Modeling ocean wave propagation under sea ice covers. Acta Mechanica Sinica, Vol. 31, Issue. 1, p. 1.


    Clark di Leoni, P. Cobelli, P. J. and Mininni, P. D. 2014. Wave turbulence in shallow water models. Physical Review E, Vol. 89, Issue. 6,


    Liu, Zeng and Liao, Shi-Jun 2014. Steady-state resonance of multiple wave interactions in deep water. Journal of Fluid Mechanics, Vol. 742, p. 664.


    Mei, Chiang C. 2014. Note on modified Zakharov’s equation accounting for scattering in disordered media. European Journal of Mechanics - B/Fluids, Vol. 47, p. 158.


    Picozzi, A. Garnier, J. Hansson, T. Suret, P. Randoux, S. Millot, G. and Christodoulides, D.N. 2014. Optical wave turbulence: Towards a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics. Physics Reports, Vol. 542, Issue. 1, p. 1.


    Humbert, T. Cadot, O. Düring, G. Josserand, C. Rica, S. and Touzé, C. 2013. Wave turbulence in vibrating plates: The effect of damping. EPL (Europhysics Letters), Vol. 102, Issue. 3, p. 30002.


    Sun, Oliver M. and Pinkel, Robert 2013. Subharmonic Energy Transfer from the Semidiurnal Internal Tide to Near-Diurnal Motions over Kaena Ridge, Hawaii. Journal of Physical Oceanography, Vol. 43, Issue. 4, p. 766.


    ×

On the non-linear energy transfer in a gravity wave spectrum Part 2. Conservation theorems; wave-particle analogy; irrevesibility

  • K. Hasselmann (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112063000239
  • Published online: 01 March 2006
Abstract

From the conditions of energy and momentum conservation it is shown that all four interaction coefficients of the elementary quadruple interactions discussed in Part I of this paper are equal. A further conservative quantity is then found which can be interpreted as the number density of the gravity-wave ensemble representing the random sea surface. The well-known analogy between a random linear wave field and a mass particle ensemble is found to hold also in the case of weak non-linear interactions in the wave field. The interaction conditions for energy transfer between waves to correspond to the equations of energy and momentum conservation for a particle collision, the final equation for the rate of change of the wave spectrum corresponding to Boltzmann's equation for the rate of change of the number density of an ensemble of colliding mass particles. The stationary wave spectrum corresponding to the Maxwell distribution for a mass particle ensemble is found to be degenerate. The question of the irreversibility of the transfer process for gravity waves is discussed but not completely resolved.

Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax