## Compatible Mathematical Models for Coastal Hydrodynamics

### Organization:

*Funded by: *NWO & STW

*PhD: **Elena Gagarina*

*Supervisor: *Onno Bokhove / Jaap van der Vegt

*Collaboration*:

### Description:

The hydrodynamics in the near-shore coastal zone concerns the water motion on the centimeter to kilometer range scales near coastlines. The effects of wave breaking on vortices and currents; dispersive wave phenomena; wave-vortex interactions; and, the flooding and drying on beaches and dikes occurring in storm surges constitute this complex near-shore hydrodynamics.The project aims to create new mathematical models to predict and analyze these phenomena in our fight to keep the nether lands dry.

The second task is to construct innovative approach to obtain (pseudo-)symplectic time integrators. We explore discontinuous finite element method to get time integrators, both for autonomous and non-autonomous systems. The variational formulation is directly associated with the conservation laws of the system, such as energy conservation and preservation of the phase space structure. Discrete variational principles will be constructed to preserve the properties of the continuum systems also at the discrete level. The main reason to investigate these numerical schemes is to obtain stable time integrators for highly nonlinear water waves.

The third task of the project is to create a numerical wave tank. We develop novel space-time (dis)continuous Galerkin methods based on variational principles to model nonlinear free surface waves. The numerical data are verified against the wave tank data of the Maritime Research Institute Netherlands.

*At the beach next to Tyne Pier near Newcastle, obliquely incident breaking waves generate a longshore current towards us. A shear concerning the vertical component of vorticity arises in the surf zone due to this breaking wave activity. Photo courtesy: O. Bokhove.*

### PHD defense:

03 October 2014, 12:45 Hours,** **Title: Variational approaches of water waves simulation

### Posters:

Gagarine, E, Bokhove, O, van der Vegt, J.J.W. “Hamiltonian water wave model with vertical vorticity” , Cambridge Workshop, 11-15 April (2011)

Bokhove, O., Gagarina E., Martin Robinson, Anthony Thornton, Jaap van der Vegt, Wout Zweers

”Bore Soliton Splash” EGU Vienna, 3-8 april ,(2011)."