A Hamiltonian Boussinesq model with horizontally sheared currents

Elena Gagarina, Jaap van der Vegt, Vijaya Ambati, Onno Bokhove

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    28 Downloads (Pure)


    We are interested in the numerical modeling of wave-current interactions around beaches’ surf zones. Any model 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 formulated the Hamiltonian dynamics of a new water wave model. This model incorporates both the shallow water model and the potential flow model as limiting systems. The variational model derived by Cotter and Bokhove (2010) is such a model, but the variables used have been difficult to work with. Our new model has a three-dimensional velocity field consisting of the full three-dimensional potential field plus horizontal velocity components, such that the vertical component of vorticity is nonzero. Our aims are to augment the new model locally with bores and to derive a numerical finite element discretization of the new model including the capturing of bores. As a preliminary step, the variational finite element discretization of Miles’ variational principle coupled to an elliptic mesh generator is shown.
    Original languageEnglish
    Title of host publicationProceedings 3rd International Symposium on Shallow Flows (ISSF)
    Subtitle of host publicationJune 4-6, 2012, University of Iowa, Iowa City, IA, USA
    Place of PublicationIowa City
    Number of pages10
    Publication statusPublished - Jun 2012
    Event3rd international Symposium on Shallow Flows, ISSF 2012 - Iowa City, United States
    Duration: 3 Jun 20126 Jun 2012
    Conference number: 3


    Conference3rd international Symposium on Shallow Flows, ISSF 2012
    Abbreviated titleISSF
    Country/TerritoryUnited States
    CityIowa City


    • Water wave model
    • Compatible schemes
    • (Dis)Continuous finite elements
    • Hamiltonian dynamics


    Dive into the research topics of 'A Hamiltonian Boussinesq model with horizontally sheared currents'. Together they form a unique fingerprint.

    Cite this