Horizontal circulation and jumps in Hamiltonian wave models

Elena Gagarina, Jacobus J.W. van der Vegt, Onno Bokhove

Research output: Book/ReportReportOther research output

5 Citations (Scopus)
8 Downloads (Pure)

Abstract

We are interested in the numerical modeling 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. Boussinesq-type simplifications of the vertical flow profile follow directly from the new Hamiltonian formulation, such as extensions of variational Boussinesq models and Green-Naghdi equations. 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.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages14
Publication statusPublished - Jan 2013

Keywords

  • METIS-296232
  • EWI-22919
  • Variational principles
  • Water waves

Cite this

Gagarina, E., van der Vegt, J. J. W., & Bokhove, O. (2013). Horizontal circulation and jumps in Hamiltonian wave models. Enschede: University of Twente, Department of Applied Mathematics.
Gagarina, Elena ; van der Vegt, Jacobus J.W. ; Bokhove, Onno. / Horizontal circulation and jumps in Hamiltonian wave models. Enschede : University of Twente, Department of Applied Mathematics, 2013. 14 p.
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abstract = "We are interested in the numerical modeling 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. Boussinesq-type simplifications of the vertical flow profile follow directly from the new Hamiltonian formulation, such as extensions of variational Boussinesq models and Green-Naghdi equations. 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.",
keywords = "METIS-296232, EWI-22919, Variational principles, Water waves",
author = "Elena Gagarina and {van der Vegt}, {Jacobus J.W.} and Onno Bokhove",
year = "2013",
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publisher = "University of Twente, Department of Applied Mathematics",

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Gagarina, E, van der Vegt, JJW & Bokhove, O 2013, Horizontal circulation and jumps in Hamiltonian wave models. University of Twente, Department of Applied Mathematics, Enschede.

Horizontal circulation and jumps in Hamiltonian wave models. / Gagarina, Elena; van der Vegt, Jacobus J.W.; Bokhove, Onno.

Enschede : University of Twente, Department of Applied Mathematics, 2013. 14 p.

Research output: Book/ReportReportOther research output

TY - BOOK

T1 - Horizontal circulation and jumps in Hamiltonian wave models

AU - Gagarina, Elena

AU - van der Vegt, Jacobus J.W.

AU - Bokhove, Onno

PY - 2013/1

Y1 - 2013/1

N2 - We are interested in the numerical modeling 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. Boussinesq-type simplifications of the vertical flow profile follow directly from the new Hamiltonian formulation, such as extensions of variational Boussinesq models and Green-Naghdi equations. 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.

AB - We are interested in the numerical modeling 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. Boussinesq-type simplifications of the vertical flow profile follow directly from the new Hamiltonian formulation, such as extensions of variational Boussinesq models and Green-Naghdi equations. 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.

KW - METIS-296232

KW - EWI-22919

KW - Variational principles

KW - Water waves

M3 - Report

BT - Horizontal circulation and jumps in Hamiltonian wave models

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

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Gagarina E, van der Vegt JJW, Bokhove O. Horizontal circulation and jumps in Hamiltonian wave models. Enschede: University of Twente, Department of Applied Mathematics, 2013. 14 p.