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.
|Title of host publication||Proceedings 3rd International Symposium on Shallow Flows (ISSF)|
|Subtitle of host publication||June 4-6, 2012, University of Iowa, Iowa City, IA, USA|
|Place of Publication||Iowa City|
|Number of pages||10|
|Publication status||Published - Jun 2012|
|Event||3rd international Symposium on Shallow Flows, ISSF 2012 - Iowa City, United States|
Duration: 3 Jun 2012 → 6 Jun 2012
Conference number: 3
|Conference||3rd international Symposium on Shallow Flows, ISSF 2012|
|Period||3/06/12 → 6/06/12|
- Water wave model
- Compatible schemes
- (Dis)Continuous finite elements
- Hamiltonian dynamics
Gagarina, E., van der Vegt, J., Ambati, V., & Bokhove, O. (2012). A Hamiltonian Boussinesq model with horizontally sheared currents. In Proceedings 3rd International Symposium on Shallow Flows (ISSF): June 4-6, 2012, University of Iowa, Iowa City, IA, USA (pp. 1-10). Iowa City: IIHR.