Mathematical techniques for linear wave-structure interactions

It is difficult not to be impressed by the sheer range of Touviah Miloh's research output, and it is all the more remarkable that he has found the time to become a regular contributor to the Water Wave Workshops over many years. Each of his contributions is characterized by the application of powerful mathematical techniques coupled with a keen sense of the underlying physics of the problem under consideration. In the spirit of this approach, this paper offers a review of some of the mathematical techniques that have been employed to tackle a variety of classical linear water-wave problems involving fixed or floating structures, and that have provided analytical or semianalytical solutions capable of useful physical interpretation. It is appropriate at this point to refer to the excellent monograph on the same topic by Chris Linton and Phil McIver (2001), and there is inevitably some overlap in choice of problems and techniques. My choice is a personal one reflecting my own interests, and I would like to apologize in advance to those colleagues whose work is not mentioned in what follows, which is primarily based on contributions from descendants of the Ursell school, which have been so prominent at these Workshops from their inception.