Violent Overtopping of Waves at Seawalls
Violent wave overtopping occurs when waves break against sea walls throwing water and spray over the top. Great Britain has hundreds of kilometres of sea walls and a high proportion have roads and railways running along them; the Cumbrian and South Devon coasts are notorious examples. Violent overtopping events can be extremely dangerous with people, cars and even trains having been washed into the sea! Waves generated by storms, either locally or offshore, exacerbated by high tides and low air pressure lead to the disruption of road and rail services, flooding, structural damage and occasionally loss of life.
The Centre for Mathematical Modelling and Flow Analysis (CMMFA) at MMU, together with the Universities of Edinburgh and Sheffield, has been funded by the EPSRC (Engineering and Physical Sciences Research Council) to investigate the violent overtopping of sea walls - the total project is worth half a million pounds. The Universities of Edinburgh and Sheffield are conducting an experimental programme while the CMMFA is developing a mathematical model to simulate overtopping events. The experimental programme is being conducted using both a 20m flume located at Edinburgh University, for two dimensional experiments, and the wave basins at HR-Wallingford for three dimensional experiments.
The Navier-Stokes equations, a coupled system of partial differential equations describing the conservation of mass, momentum and energy in a fluid, can be used to describe wave overtopping events. These equations cannot be solved analytically, so computational techniques must be used. Traditionally the depth averaged (or shallow water) form of the Navier-Stokes equations has been used to model water waves but these equations are not valid once the waves break, so a new model must be developed. MMU is developing a new method which will accurately track the water surface, even after the wave breaks. This method will provide a tool which will help engineers to design sea defences and assess coastlines which are at risk from violent overtopping.
