The ocean waves are the last great unexploited source of renewable energy. Exploiting them would ease climate change – we therefore owe it to our grandchildren to look into this matter, for they will surely be sore at us for wasting all the oil and gas on limousines and other frivolities. Technically, wave energy is the most mathematical of the renewable energy problems, because ocean waves are essentially turbulence-free. It is therefore particularly appropriate for this forum - Isaac Newton himself and many of his successors have been interested in ocean waves. In recent times James Lighthill in particular, has been prominent for his interest in waves in fluids, including the problems of wave power.

The linear theory of water waves illuminates the subject of wave power – it shows how the capture-width of a wave energy converter (WEC) is inherently limited to a certain multiple of the wavelength, depending on the pattern of its wave radiation in the far field. And it shows how a wave energy converter must also be a good radiator of wave power. It also shows that the power of a WEC is inherently linked to the wave force on it, times the particle velocity in the incoming waves. This shows why wave energy is inherently more challenging that wind power – it is because average wave particle velocities are much lower than wind speeds.

From this theoretical standpoint, the present generation of WECs appear logical enough. It also shows why they must inherently be non-linear – an important recent innovation. And, perhaps, it points the way to a new generation of WECs, with radically better economics.

This talk will follow a welcome introduction and is part of the UK Launch of Mathematics of Planet Earth 2013. More info @ www.newton.ac.uk/events/2013/mpe/