Summary
In this paper a new shallow water wave model is described which uses nonlinear dissipation derived from turbulent diffusion as damping mechanism. The source functions of the model are presented in detail. Analytical results of the dynamical equation for simple cases illustrate basic features of the model. Academic test runs in deep and shallow water are performed. The designed cases are identical to the ones used in previous wave model intercomparison studies and thus allow comparison with other wave models. Results of a hindcast of a North Sea storm event illustrate the model behaviour in nonuniform real shallow water systems. In this case we can compare with field data and with the community wave model WAM cy. 4, which has been run parallel to our model. Our study shows that the concept of wave modelling with nonlinear dissipation is consistent with common knowledge of wave evolution in oceanic and shelf sea applications.
Zusammenfassung
Ein neues Seegangsmodell für Flachwasser wird beschrieben, welches nichtlineare Dissipation durch turbulente Diffusion als DÄmpfungsmechanismus verwendet. Die Quellfunktionen werden im Detail angegeben. Analytische Lösungen der dynamischen Gleichung in einfachen FÄllen illustrieren prinzipielle Eigenschaften des Modells. Akademische Tests für tiefes und flaches Wasser werden durchgeführt. Die Tests können mit entsprechenden Rechnungen aus früheren Modellvergleichsstudien verglichen werden. Die Nachrechnung eines Nordseesturmes zeigt das Verhalten des Modells in realen nichtuniformen Systemen. Ein Vergleich mit Felddaten und Ergebnissen des Community-Modells WAM cy. 4, welches parallel zum Einsatz gebracht wurde, kann durchgeführt werden. Unsere Studie zeigt, da\ das Konzept der Seegangsmodellierung mit nichtlinearer Dissipation zu Ergebnissen führt, die dem allgemeinen VerstÄndnis von Seegang in globalen und regionalen Anwendungen entsprechen.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Battjes, J. A. and J. P. F. M. Janssen, 1978: Energy loss and set-up due to breaking of random waves. In: Proc. 16th Int. Conf. Coastal Engineering, pages 569-587, Hamburg, 1978.
Bender, L. C., 1996: Modification of the physics and numerics in a third-generation ocean wave model.J. Atmos. Oceanic Technol.,13, 726–750.
Bouws, E., H. Günther, andW. Rosenthal, 1985: Similarity of the wind wave spectrum in finite depth water. 1. Spectral form.J. Geophys. Res.,90, 975–986.
Burgers, G. andV. K. Makin, 1992: Boundary layer model results for wind-sea growth.J. Phys. Oceanogr.,23, 372–385.
Cavaleri, L.. andP. Manalotte Rizzoli, 1981: Wind wave prediction in shallow water — theory and application.J. Geophys. Res.,86, 10961.
Eldeberky, Y. and J. A. Battjes, 1995: Parameterisation of triad interactions in wave energy models. In: Proc. Int. Conf. Coastal Dynamics, pages 569–587, Gdansk, Poland.
Eldeberky, Y.. andJ. A. Battjes, 1996: Spectral modelling of wave breaking: Application to boussinesq equations.J. Geophys. Res.,101, 1253–1264.
Günther, H., S. Hasselmann, and P. A. E. M. Janssen, 1992: The WAM Model cycle 4.0. User manual. Deutsches Klimarechenzentrum Hamburg, technical report no. 4.
Günther, H. and W. Rosenthal, 1995: A wave model with a non-linear dissipation source function. In: Proc. 4th Int. Workshop Wave Hindcasting and Forecasting, Banff, Canada.
Hasselmann, K.., 1974: On the spectral dissipation of ocean waves due to white capping.Boundary-Layer Meteorol.,6, 107–127.
Hasselmann, K., T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright, K. Enke, J. A. Ewing, H. Gienapp, D. E. Hasselmann, P. Krusemann, A. Meerburg, P. Mueller, D. J. Olbers, K. Richter, W. Sell, and H. Walden, 1973: Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP).Dt. Hydrogr. Z. Erg.-H.,A8 (12), 95p.
Holthuijsen, L. H., N. Booij, and R. C. Ris, 1993: A spectral model for the tidal zone. In: Proc. Int. Conf. WAVES.
Holthuijsen, L. H., N. Booij, and R. C. Ris, 1996: User manual of the program SWAN cycle 1, simulation of waves in the near-shore. Faculty of Civil Engineering, Delft University of Technology, the Netherlands.
Kahma, K. K.. andC. J. Calkoen, 1992: Reconciling discrepancies in the observed growth of wind-generated waves.J. Phys. Oceanogr.,22, 1389–1405.
Komen, G. J., L. Cavaleri, M. Donelan, K. Hasselmann, S. Hasselmann, and P. A. E. M. Janssen, 1994: Dynamics and Modelling of Ocean Waves. Cambridge University Press.
Lin, R. Q.. andN. E. Huang, 1996: The Goddard Coastal Wave Model. Part I: Numerical method.J. Phys. Oceanogr.,26, 833–847.
Miles, J. W., 1957: On the generation of surface waves by shear flows.J. Geophys. Res.,99, 18501–18511.
Phillips, O. M., 1957: On the generation of waves by turbulent wind.J. Fluid Mech.,2, 417–445.
Phillips, O..M. Phillips, 1985: Spectral and statistical properties of the equilibrium range in wind-generated gravity waves.J. Fluid Mech.,156, 505–531.
Pierson, W. J.., Jr. andL. Moskowitz, 1964: A proposed spectral form for fully developed wind seas based on the similarity theory of S. A. Kitaigorodskii.J. Geophys. Res.,69, 5181–5190.
Plant, W. J., 1986: A two-scale model of short wind-generated waves and scatterometry.J. Geophys. Res.,91, 10735–10749.
Rosenthal, W., 1989: Derivation of Phillips α-parameter from turbulent diffusion as a damping mechanism. In: G. J. Komen and W. A. Oost, editors, Radar Scattering from Modulated Wind Waves, pages 81-88. Kluwer Academic Publishers.
Shemdin, O., K. Hasselmann, S. V. Hsiao, and K. Herterich, 1978: Nonlinear and linear bottom interaction effects in shallow water. In: A. Favre and K. Hasselmann, editors, Proc. NATO Symp. on Turbulent Fluxes through the Sea Surface, Wave Dynamics, and Prediction, Ile de Bendor, France, Plenum Press.
Snyder, R. L..,F. W. Dobson, J. A. Elliott, andR. B. Long, 1981: Array measurements of atmospheric pressure fluctuations above surface gravity waves.J. Fluid Mech.,102, 1–59.
Snyder, R. L..,L. M. Lawson, andR. B. Long, 1992: Inverse modelling of the action-balance equation. Part I: Source expansion and adjoint model equations.J. Phys. Oceanogr.,22, 1540–1555.
SWAMP, 1985: The SWAMP group: J. H. Allender, T. P. Barnett, L. Bertotti, J. Bruinsma, V. J. Cardone, L. Cavaleri, J. Ephraums, B. Golding, A. Greenwood, J. Guddal, H. Guenther, K. Hasselmann, S. Hasselmann, P. Joseph, S. Kawai, G. J. Komen, L. Lawson, Linné, R. B. Long, M. Lybanon, E. Maeland, W. Rosenthal, Y. Toba, T. Uji, and W. J. P. de Voogt. Ocean Wave Modelling. Plenum Press.
SWIM, 1985: The SWIM group:E. Bouws, J. J. Ephraums, J. A. Ewing, P. E. Francis, H. Guenther, P. A. E. M. Janssen, G. J. Komen, W. Rosenthal, andW. J. P. de Voogt. A shallow water intercomparison of three numerical wave prediction models (SWIM). Quart.J. R. Met. Soc.,111, 1087–1112.
WAMDI, 1988: The WAMDI group:S. Hasselmann, K. Hasselmann, E. Bauer, P. A. E. M. Janssen, G. J. Komen, L. Bertotti, P. Lionello, A. Guillaume, V. C. Car-done, J. A. Greenwood, M. Reistad, L. Zambresky, andJ. A. Ewing. The WAM model — a third generation ocean wave prediction model.J. Phys. Oceanogr.,18, 1775–1810.
Toba, Y., 1973: Local balance in the air-sea boundary process, 3. On the spectrum of wind waves.Oceanogr. Soc.,29, 209–220.
Tolman, H. L., 1992: Effects of numerics on the physics in a third-generation wind-wave model.J. Phys. Oceanogr.,22, 1095–1111.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Schneggenburger, C., Günther, H. & Rosenthal, W. Shallow water wave modelling with nonlinear dissipation. Deutsche Hydrographische Zeitschrift 49, 431–444 (1997). https://doi.org/10.1007/BF02764049
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02764049