Skip to main content

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
Cancel
×
×
Home
  • Home
Article
  • Cited by 24
  • Cited by
    Crossref Citations
    Crossref logo
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Lewis, Huw W. Castillo Sanchez, Juan Manuel Graham, Jennifer Saulter, Andrew Bornemann, Jorge Arnold, Alex Fallmann, Joachim Harris, Chris Pearson, David Ramsdale, Steven Martínez-de la Torre, Alberto Bricheno, Lucy Blyth, Eleanor Bell, Victoria A. Davies, Helen Marthews, Toby R. O'Neill, Clare Rumbold, Heather O'Dea, Enda Brereton, Ashley Guihou, Karen Hines, Adrian Butenschon, Momme Dadson, Simon J. Palmer, Tamzin Holt, Jason Reynard, Nick Best, Martin Edwards, John and Siddorn, John 2018. The UKC2 regional coupled environmental prediction system. Geoscientific Model Development, Vol. 11, Issue. 1, p. 1.
    Campos, R.M. Alves, J.H.G.M. Guedes Soares, C. Guimaraes, L.G. and Parente, C.E. 2018. Extreme wind-wave modeling and analysis in the south Atlantic ocean. Ocean Modelling, Vol. 124, Issue. , p. 75.
    Janssen, Peter A.E.M. and Bidlot, Jean-Raymond 2018. Progress in Operational Wave Forecasting. Procedia IUTAM, Vol. 26, Issue. , p. 14.
    Kazeminezhad, Mohammad Hossein and Siadatmousavi, Seyed Mostafa 2017. Performance evaluation of WAVEWATCH III model in the Persian Gulf using different wind resources. Ocean Dynamics, Vol. 67, Issue. 7, p. 839.
    Seemanth, M. Bhowmick, Suchandra Aich Kumar, Raj and Sharma, Rashmi 2016. Sensitivity analysis of dissipation parameterizations in a third-generation spectral wave model, WAVEWATCH III for Indian Ocean. Ocean Engineering, Vol. 124, Issue. , p. 252.
    Pushkarev, Andrei and Zakharov, Vladimir 2016. Limited fetch revisited: Comparison of wind input terms, in surface wave modeling. Ocean Modelling, Vol. 103, Issue. , p. 18.
    Lee, Han Soo 2015. Evaluation of WAVEWATCH III performance with wind input and dissipation source terms using wave buoy measurements for October 2006 along the east Korean coast in the East Sea. Ocean Engineering, Vol. 100, Issue. , p. 67.
    Bi, Fan Song, Jinbao Wu, Kejian and Xu, Yao 2015. Evaluation of the simulation capability of the Wavewatch III model for Pacific Ocean wave. Acta Oceanologica Sinica, Vol. 34, Issue. 9, p. 43.
    Mentaschi, Lorenzo Besio, Giovanni Cassola, Federico and Mazzino, Andrea 2015. Performance evaluation of Wavewatch III in the Mediterranean Sea. Ocean Modelling, Vol. 90, Issue. , p. 82.
    Janssen, P. A. E. M. 2012. Ocean wave effects on the daily cycle in SST. Journal of Geophysical Research: Oceans, Vol. 117, Issue. C11, p. n/a.
    Troitskaya, Yu. Sergeev, D. Ermakova, O. and Balandina, G. 2011. Statistical Parameters of the Air Turbulent Boundary Layer over Steep Water Waves Measured by the PIV Technique. Journal of Physical Oceanography, Vol. 41, Issue. 8, p. 1421.
    KIHARA, Naoto HANAZAKI, Hideshi and HIRAKUCHI, Hiromaru 2011. Simulation of Airflow over Superposed Wave Train with Different Wave Lengths. TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series B, Vol. 77, Issue. 776, p. 1075.
    YANG, DI and SHEN, LIAN 2010. Direct-simulation-based study of turbulent flow over various waving boundaries. Journal of Fluid Mechanics, Vol. 650, Issue. , p. 131.
    Cavaleri, Luigi 2009. Wave Modeling—Missing the Peaks. Journal of Physical Oceanography, Vol. 39, Issue. 11, p. 2757.
    Kukulka, Tobias and Hara, Tetsu 2008. The Effect of Breaking Waves on a Coupled Model of Wind and Ocean Surface Waves. Part I: Mature Seas. Journal of Physical Oceanography, Vol. 38, Issue. 10, p. 2145.
    Cavaleri, L. Alves, J.-H.G.M. Ardhuin, F. Babanin, A. Banner, M. Belibassakis, K. Benoit, M. Donelan, M. Groeneweg, J. Herbers, T.H.C. Hwang, P. Janssen, P.A.E.M. Janssen, T. Lavrenov, I.V. Magne, R. Monbaliu, J. Onorato, M. Polnikov, V. Resio, D. Rogers, W.E. Sheremet, A. McKee Smith, J. Tolman, H.L. van Vledder, G. Wolf, J. and Young, I. 2007. Wave modelling – The state of the art. Progress in Oceanography, Vol. 75, Issue. 4, p. 603.
    Yu, Weidong Li, Zhaoxin and Yuan, Yeli 2005. Improvement of the SLP simulation in the coupled AGCM-ocean surface wave model. Chinese Science Bulletin, Vol. 50, Issue. 20, p. 2397.
    McIntyre, M.E. 2003. Wind over Waves II. p. 105.
    Bourassa, Mark A. Vincent, Dayton G. and Wood, W. L. 2001. A Sea State Parameterization with Nonarbitrary Wave Age Applicable to Low and Moderate Wind Speeds. Journal of Physical Oceanography, Vol. 31, Issue. 10, p. 2840.
    Belcher, S. E. and Hunt, J. C. R. 1998. TURBULENT FLOW OVER HILLS AND WAVES. Annual Review of Fluid Mechanics, Vol. 30, Issue. 1, p. 507.
    Download full list
    ×
  • Get access
    Add to cart USD35.00
    Check if you have access via personal or institutional login
    Log in Register Recommend to librarian

Quasilinear approximation for the spectrum of wind-generated water waves

  • Peter A. E. M. Janssen (a1)
Abstract

According to Miles’ theory of wind-wave generation, water waves grow if the curvature of the wind profile at the critical height is negative. As a result, the wind profile changes in time owing to the transfer of energy to the waves. In the quasilinear approximation (where the interaction of the waves with one another is neglected) equations for the coupled air–water system are obtained by means of a multiple-time-scale analysis. In this way the validity of Miles’ calculations is extended, thereby allowing a study of the large-time behaviour.

While the water waves grow owing to the energy transfer from the air flow, the waves in turn modify the flow in such a way that for large times the curvature of the velocity profile vanishes. The amplitude of the waves is then limited because the energy transfer is quenched.

In the high-frequency range the asymptotic wave spectrum is given by a ‘–4’ law in the frequency domain rather than the ‘classical’ ‘–5’ law.

Copyright
© 1982 Cambridge University Press
References
Hide All
Bernstein, I. B. & Engelmann, F. 1966 Quasi-linear theory of plasma waves. Phys. Fluids 9, 937.
Davidson, R. C. 1972 Methods in Nonlinear Plasma Theory. Academic.
Drummond, W. E. & Pines, D. 1962 Nonlinear stability of plasma oscillations. Nucl. Fusion Soc Suppl. 3, 1049.
Fabrikant, A. L. 1976 Quasilinear theory of wind-wave generation. Izv., Atmos. Oceanic Phys. 12, 524.
Hasselmann, K. 1967 Nonlinear interactions treated by the methods of theoretical physics (with application to the generation of waves by wind). Proc. R. Soc. Lond. A 299, 77.
Hasselmann, K. 1974 On the spectral dissipation of ocean waves due to white capping. Boundary-layer Met. 6, 107.
Hasselmann, K. 1978 On the spectral energy balance and numerical prediction of ocean waves. In Turbulent Fluxes through the Sea Surface, Wave Dynamics, and Prediction (ed. A. Favre & K. Hasselmann), p. 531. Plenum.
Hasselmann, K., Barnett, T. P., Bouws, E., Carlson, H., Cartwright, D. E., Enke, K., Ewing, J. A., Gienapp, H., Hasselmann, D. E., Kruseman, P., Meerburg, A., Müller, P., Olbers, D. J., Richter, K., Sell, W. & Walden, H. 1973 Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Deutsche Hydrog. Z., Suppl. A (80), no. 12.
Landau, L. 1946 On the vibrations of the electronic plasma. J. Phys. (U.S.S.R) 10, 25.
Lighthill, M. J. 1962 Physical interpretation of the mathematical theory of wave generation by wind. J. Fluid Mech. 14, 385.
Miles, J. W. 1957 On the generation of surface waves by shear flows. J. Fluid Mech. 3, 185.
Mitsuyasu, H., Tasai, F., Suhara, T., Mizuno, S., Ohkusu, M., Honda, T. & Rikushi, K. 1980 Observation of the power spectrum of ocean waves using a cloverleaf buoy. J. Phys. Oceanog. 10, 286.
Phillips, O. M. 1958 The equilibrium range in the spectrum of wind-generated water waves. J. Fluid Mech. 4, 426–434.
Snyder, R. L., Dobson, F. W., Elliot, J. A. & Long, R. B. 1981 Array measurements of atmospheric pressure fluctuations above surface gravity waves. J. Fluid Mech. 102, 1.
Stewart, R. W. 1967 Mechanics of the air-sea interface. Phys. Fluids Suppl. 10, S47.
Toba, Y. 1973 Local balance in the air-sea boundary processes. III. On the spectrum of wind waves. J. Oceanog. Soc. Japan 29, 209.
Toba, Y. 1978 Stochastic form of the growth of wind waves in a single-parameter representation with physical implications. J. Phys. Oceanog. 8, 494.
Vedenov, A. A., Velikhov, E. P. & Sagdeev, R. Z. 1961 Nonlinear oscillations of a rarefied plasma. Nucl. Fusion 1, 182.
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? *

CAPTCHA *

Skip to the audio challenge
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 28 *
Loading metrics...

Abstract views

Total abstract views: 120 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 12th June 2018. This data will be updated every 24 hours.

Cancel
Confirm
×