Wave Phenomena

I am interested in problems relating to the interaction of waves with structures in a variety of settings including fluids, elasticity, electromagnetics and acoustics. The main application areas are:

1. Marine renewables, specifically the harnessing of ocean wave energy. Analysing the efficacy of current wave energy devices and developing new wave energy converter ideas based on theoretical results.
2. Elasticity, waves in elastic plates and ocean wave interaction with floating ice.
3. Cloaking and metamaterials in water waves.
4. Methods for studying ocean wave propagation over variable bathymetry.
5. The interaction of ocean waves with very large structures where computational methods are prohibitively expensive.
6. Trapped waves, edge waves and near resonance in wave/structure interactions.

PhD Projects

Controlling waves using metamaterials

About 5 years I started looking at invisibility cloaking in water waves and in 2016 I wrote a review article on the subject. There are many exciting things you can do with water waves which have hardly been touched upon because they rely on controlling waves using conditions which don't occur in natural settings. These are realised by the use of metamaterials. So, for example, the depth of the ocean can have two values depending on which way the wave is travelling. Or gravity can be altered in space. There are lots of problems which can be considered once you expand the range of conditions of the problem to include metamaterials.

Harnessing the Power of Ocean Waves

A research passion of mine: using mathematics to understand and develop the design of wave energy converters. My past two PhD students have done projects on how to harness the energy in ocean waves. I would like to consider a project which considers the efficacy of very large arrays of small wave energy converters. It relates to work by Garnaud and Mei (2010) and Carter and McIver (2013).