Sea wave energy is being increasingly regarded in many countries as a major and promising resource. The paper deals with the development of wave energy utilization since the 1970s. Several topics are addressed: the characterization of the wave energy resource; theoretical background, with especial relevance to hydrodynamics of wave energy absorption and control; how a large range of devices kept being proposed and studied, and how such devices can be organized into classes; the conception, design, model-testing, construction and deployment into real sea of prototypes; and the development of specific equipment (air and water turbines, high-pressure hydraulics, linear electrical generators) and mooring systems.

Wave energy utilization: A review of the technologies

Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

Bound states in the continuum (BICs) are waves that remain localized even though they coexist with a continuous spectrum of radiating waves that can carry energy away. Their very existence defies conventional wisdom. Although BICs were first proposed in quantum mechanics, they are a general wave phenomenon and have since been identified in electromagnetic waves, acoustic waves in air, water waves and elastic waves in solids. These states have been studied in a wide range of material systems, such as piezoelectric materials, dielectric photonic crystals, optical waveguides and fibres, quantum dots, graphene and topological insulators. In this Review, we describe recent developments in this field with an emphasis on the physical mechanisms that lead to BICs across seemingly very different materials and types of waves. We also discuss experimental realizations, existing applications and directions for future work. The fascinating wave phenomenon of ‘bound states in the continuum’ spans different material and wave systems, including electron, electromagnetic and mechanical waves. In this Review, we focus on the common physical mechanisms underlying these bound states, whilst also discussing recent experimental realizations, current applications and future opportunities for research.

Bound states in the continuum

United States. Army Research Office (Institute for Soldier Nanotechnologies under contract no. W911NF-07-D0004)

https://www.mit.edu/~soljacic/trapped-light_Nature.pdf

Observation of trapped light within the radiation continuum

A review of wave-energy extraction

Some general results are derived for the efficiency of energy absorption of a system of uniform oscillatory surface pressure distributions. The results, which are based on classical linear water-wave theory, show the close analogies which exist with theories for systems of absorbing oscillatory rigid bodies and a number of new reciprocal relations for pressure distributions are suggested and proved. Some simple examples illustrating the general results are given and compared with the corresponding results for rigid bodies.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112082000263

Wave-power absorption by systems of oscillating surface pressure distributions

A two-dimensional acoustic waveguide of infinite extent described by two parallel lines contains an obstruction of fairly general shape which is symmetric about the centreline of the waveguide. It is proved that there exists at least one mode of oscillation, antisymmetric about the centreline, that corresponds to a local oscillation at a particular frequency, in the absence of excitation, which decays with distance down the waveguide away from the obstruction. Mathematically, this trapped mode is related to an eigenvalue of the Laplace operator in the waveguide. The proof makes use of an extension of the idea of the Rayleight quotient to characterize the lowest eigenvalue of a differential operator on an infinite domain.

/pdf/existence-theorems-for-trapped-modes-32kghnxnqm.pdf

Existence theorems for trapped modes

The scattering of water waves by an array of N bottom-mounted vertical circular cylinders is solved exactly (under the assumption of linear water wave theory) using the method proposed by Spring & Monkmeyer in 1974. A major simplification to this theory has been found which makes the evaluation of quantities such as the forces on the cylinders much simpler. New formulae are given for the first and mean second-order forces together with one for the free-surface elevation in the vicinity of a particular cylinder. Comparisons are made between the exact results shown here and those generated using the approximate method of McIver & Evans (1984). The behaviour of the forces on the bodies in the long-wave limit is also examined for the special case of two cylinders with equal radii.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112090002750

D. V. Evans

Papers

Wave-power absorption by systems of oscillating surface pressure distributions

Existence theorems for trapped modes

The interaction of waves with arrays of vertical circular cylinders

Hydrodynamic characteristics of an oscillating water column device

The Oscillating Water Column Wave-energy Device