 
Summary: Hamiltonian water wave model with vertical
vorticity
Elena Gagarina, Onno Bokhove, Jaap van der Vegt
Numerical Analysis and Computational Mechanics Group
Department of Applied Mathematics
Universtity of Twente, Enschede, The Netherlands
Motivation
Figure 1: The tidal bore in Upper Cook Inlet. Photo: S. Nicklas.
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 models using the 2D horizontal coordinates
and time.
· Variables are depth h and depthaveraged horizontal velocity u.
· Bores and hydraulic jumps arise as a simplified model of breaking
waves.
Figure 2: Undular bore on River Severn. Photo: D.H. Peregrine.
