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| Titel |
Fully nonlinear water waves of high amplitude, propagating in finite depth |
| VerfasserIn |
Gerassimos Athanassoulis, Konstantinos Belibassakis |
| Konferenz |
EGU General Assembly 2011
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 13 (2011) |
| Datensatznummer |
250053787
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| Zusammenfassung |
| The nonlinear, coupled-mode equations, developed by the authors (Athanassoulis &
Belibassakis 2002, 2007), modelling the evolution of nonlinear water waves over a general
bottom topography, are applied to the investigation of fully nonlinear waves of
high-amplitude propagating in constant water depth. The vertical structure of the wave field is
represented by means of a local-mode series expansion of the wave potential. This series
contains the usual propagating and evanescent modes, plus an additional term, the
free-surface mode, enabling to consistently treat the boundary conditions at the free surface.
The role and significance of the additional free-surface mode, particularly concerning the
fast rate of convergence of the modal series, is proved analytically and illustrated
numerically.
In the present work, the coupled-mode system is applied to the numerical investigation of
propagating waves in constant depth, from intermediate depth to shallow-water conditions. A
variational reformulation of the complete, potential, non-linear water-wave equations is
solved iteratively, with appropriate step-by-step adjustment of the propagation speed. The
results are compared vs. Stokes and cnoidal wave theories (Fenton 1990), as well as vs. fully
nonlinear Fourier schemes (e.g., Rienecker & Fenton 1981). A method is also developed for
the determination of the nonlinear dispersion characteristics of steady travelling waves, and
comparisons are presented with the corresponding approximate results obtained by various
wave theories. Finally, the extension of the present method for modelling 3D fully non-linear
waves is discussed.
References
Athanassoulis G.A., Belibassakis K.A, 2002. A nonlinear coupled-mode model for water
waves over a general bathymetry, Proc. 21st Int. Conf. on Offshore Mechanics and Arctic
Engineering, OMAE2002, Oslo, Norway 2002.
Athanassoulis G.A., Belibassakis K.A., 2007. A coupled-mode method for
non-linear water waves in general bathymetry with application to steady travelling
solutions in constant, but arbitrary, depth, J. Discrete and Continuous Dynamical
Systems DCDS-B, 75-84 (special volume of selected papers from 6th Int. Conference
on Dynamical Systems and Differential Equations, Poitiers Meeting, June 25-28,
2006).
Fenton J.D., 1990. Nonlinear wave theories, in Mehaute, B., Hanes, D. (ed.) “The Sea”,
Vol. 9A, J. Wiley & Sons.
Rienecker M.M., Fenton J.D., 1981. A Fourier approximation method for steady water
waves, Journal of Fluid Mechanics 104, 119–137. |
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