 
Summary: Hamiltonian water wave model with vertical
vorticity and bores
Elena Gagarina, Onno Bokhove, Jaap van der Vegt
Mathematics of Computational Science Group
Department of Applied Mathematics
Universtity of Twente, Enschede, The Netherlands
Motivation
Figure 1: BoreSolitonSplash experiment [8]. Photo: W. Zweers.
Many water wave problems require the combination of different
mathematical models.
On the one hand:
· Depthaveraged shallow water equations (SWE) are a workhorse
in coastal engineering.
· Shallow means horizontal scales >> vertical ones.
· SWE are simplified using the 2D horizontal coordinates and time.
· Variables are depth h and depthaveraged horizontal velocity Żu.
· Bores, hydraulic jumps arise as a simplified model of breaking
waves, Figs. 1, 2.
Figure 2: Undular bore on River Severn. Photo: D.H. Peregrine.
On the other hand:
