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| Titel |
Horizontal circulation and jumps in Hamiltonian wave models |
| VerfasserIn |
E. Gagarina, J. Vegt, O. Bokhove |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 20, no. 4 ; Nr. 20, no. 4 (2013-07-12), S.483-500 |
| Datensatznummer |
250018985
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| Publikation (Nr.) |
 copernicus.org/npg-20-483-2013.pdf |
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| Zusammenfassung |
| We are interested in the modelling of wave-current interactions around surf
zones at beaches. Any model that aims to predict the onset of wave breaking
at the breaker line needs to capture both the nonlinearity of the wave and
its dispersion. We have therefore formulated the Hamiltonian dynamics of a
new water wave model, incorporating both the shallow water and pure potential
flow water wave models as limiting systems. It is based on a Hamiltonian
reformulation of the variational principle derived by Cotter and Bokhove
(2010) by using more convenient variables. Our new model has a three-dimensional velocity
field consisting of the full three-dimensional potential velocity field plus
extra horizontal velocity components. This implies that only the vertical
vorticity component is nonzero. Variational Boussinesq models and
Green–Naghdi equations, and extensions thereof, follow directly from the new
Hamiltonian formulation after using simplifications of the vertical flow
profile. Since the full water wave dispersion is retained in the new model,
waves can break. We therefore explore a variational approach to derive jump
conditions for the new model and its Boussinesq simplifications. |
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