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Imbalance of Energy and Momentum Source Terms of the Sea Wave Transfer Equation for Fully Developed Seas : Volume 8, Issue 6 (13/12/2012)

By Caudal, G. V.

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Book Id: WPLBN0004020560
Format Type: PDF Article :
File Size: Pages 14
Reproduction Date: 2015

Title: Imbalance of Energy and Momentum Source Terms of the Sea Wave Transfer Equation for Fully Developed Seas : Volume 8, Issue 6 (13/12/2012)  
Author: Caudal, G. V.
Volume: Vol. 8, Issue 6
Language: English
Subject: Science, Ocean, Science
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Historic
Publication Date:
2012
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications

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Caudal, G. V. (2012). Imbalance of Energy and Momentum Source Terms of the Sea Wave Transfer Equation for Fully Developed Seas : Volume 8, Issue 6 (13/12/2012). Retrieved from http://www.ebooklibrary.org/


Description
Description: Université Versailles-St-Quentin; CNRS/INSU, UMR8190, Laboratoire Atmosphères, Milieux, Observations Spatiales – LATMOS-IPSL 11 Boulevard d'Alembert, 78280 Guyancourt, France. In the concept of full development, the sea wave spectrum is regarded as a nearly stationary solution of the wave transfer equation, where source and sink terms should be in balance with respect to both energy and momentum. Using a two-dimensional empirical sea wave spectral model at full development, this paper performs an assessment of the compatibility of the energy and momentum budgets of sea waves over the whole spectral range. Among the various combinations of model functions for wave breaking and wind source terms tested, not one is found to fulfill simultaneously the energy and momentum balance of the transfer equation. Based on experimental and theoretical grounds, wave breaking is known to contribute to frequency downshift of a narrow-banded wave spectrum when the modulational instability is combined with wave breaking. On those grounds, it is assumed that, in addition to dissipation, wave breaking produces a spectral energy flux directed toward low wavenumbers. I show that it is then possible to remove the energy and momentum budget inconsistency, and correspondingly the required strength of this spectral flux is estimated. Introducing such a downward spectral flux permits fulfilling both energy and momentum balance conditions. Meanwhile, the consistency between the transfer equation and empirical spectra, estimated by means of a cost function K, is either improved or slightly reduced, depending upon the wave breaking and wind source terms chosen. Other tests are performed in which it is further assumed that wave breaking would also be associated with azimuthal diffusion of the spectral energy. This would correspondingly reduce the required downward spectral flux by a factor of up to 5, although it would not be able to remove it entirely.

Summary
Imbalance of energy and momentum source terms of the sea wave transfer equation for fully developed seas

Excerpt
Banner, M. L., Gemmrich, J. R., and Farmer, D. M.: Multiscale measurements of ocean wave breaking probability, J. Phys. Oceanogr., 32, 3364–3375, 2002.; Banner, M. L., Jones, I. S. F., and Trinder, J. C.: Wavenumber spectra of short gravity waves, J. Fluid Mech., 198, 321–344, 1989.; Alber, I. E.: The effect of randomness on the stability of two-dimensional surface wavetrains, P. Roy. Soc. Lond. Ser. A, 363, 525–546, 1978.; Banner, M.: Equilibrium spectra of wind waves, J. Phys. Oceanogr., 20, 966–984, 1990.; Ardhuin, F., Chapron, B., and Collard, F.: Observation of swell dissipation across oceans, Geophys. Res. Lett., 36, L06607, doi:10.1029/2008GL037030, 2009.; Ardhuin, F., Rogers, E., Babanin, A. V., Filipot, J. F., Magne, R., Roland, A., van der Westhuysen, A., Queffeulou, P., Lefevre, J. M., Aouf, L., and Collard, F.: Semi-empirical Dissipation Source Functions for Ocean Waves, Part I: Definition, Calibration, and Validation, J. Phys. Oceanogr., 40, 1917–1941, 2010.; Banner, M. L. and Morison, R. P.: Refined source terms in wind wave models with explicit wave breaking prediction, Part I: Model framework and validation against field data, Ocean Model., 33, 177–189, 2010.; Belcher, S. E. and Hunt, J. C. R.: Turbulent shear flow over slowly moving waves, J. Fluid Mech., 251, 109–148, 1993.; Benjamin, T. B. and Feir, J. E.: The disintegration of wave trains on deep water. Part 1. Theory, J. Fluid Mech. 27, 417–430, 1967.; Cox, C. and Munk, W.: Measurement of the roughness of the sea surface from photographs of the Sun's glitter, J. Opt. Soc. Am., 44, 838–850, 1954.; Donelan, M. A. and Pierson, Jr., W. J.: Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry, J. Geophys. Res., 92, 4971–5029, 1987.; Donelan, M. A., Hamilton, J., and Hui, W. H.: Directional spectra of wind generated waves, P. T. Roy. Soc. Lond. Ser. A, 315, 509–562, 1985.; Dore, B. D.: Some effects of the air-water interface on gravity waves, Geophys. Astrophys. Fluid Dynam., 10, 215–230, 1978.; Dysthe, K. B., Trulsen, K., Krogstad, H. E., and Socquet-Juglard, H.: Evolution of a narrow-band spectrum of random surface gravity waves, J. Fluid Mech., 478, 1–10, 2003.; Elfouhaily, T., Chapron, B., Katsaros, K., and Vandemark, D.: A unified directional spectrum for long and short wind-driven waves, J. Geophys. Res., 102, 15781–15796, 1997.; Gelci, R., Cazalé, H., and Vassal, J.: Prévision de la houle. La méthode des densités spectroangulaires, Bull. Infor. Comité Central Oceanogr. D'Etude Côtes, 9, 416–435, 1957.; Hara, T. and Belcher, S. E.: Wind forcing in the equilibrium range of wind-wave spectra, J. Fluid Mech., 470, 223–245, 2002.; Hasselmann, K.: On the nonlinear energy transfer in a gravity-wave spectrum, Part 1: General theory, J. Fluid Mech., 12, 481–500, 1962.; Hasselmann, K.: On the nonlinear energy transfer in a gravity-wave spectrum, Part 2: Conservation theorems; wave-particle analogy; irreversibility, J. Fluid Mech., 15, 273–281, 1963.; Hasselmann, K.: On the spectral dissipation of ocean waves due to white capping, Bound.-Lay. Meteorol., 6, 107–127, 1974.; Huang, N. E., Long, S. R., and Shen, Z.: The mechanism for frequency downshift in nonlinear wave evolution, Adv. Appl. Mech., 32, 59–117, 1996.; Hasselmann, K., Janssen, P. A. E. M., and Komen, G. J.: II, Wave-wave interaction, in Dynamics and Modeling of Ocean Waves, edited by: Komen, G. J., Cavaleri, L., Donelan, M., Hasselmann, K., Hasselmann, S., and Janssen, P. A. E. M., 113–143, Cambridge University Press, New York, 1994.; Hauser, D., Caudal, G., Guimbard, S., and Mouche A. A.: A study of the slope probability density function of the ocean waves from radar observations, J. Geophys. Res., 113, C02006, doi:10.1029/2007JC004264, 2008.; Jähne, B. and Riemer, K. S.: Two-dimensional wave number spectra of small-scale water surfac

 

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