A review of wave-energy extraction

Abstract

Comparing ocean-wave energy with its origin, wind energy, the former is more persistent and spatially concentrated. In this paper wave spectrum parameters related to transport, distribution and variability of wave energy in the sea are educed. Many different types of wave-energy converters, of various categories, have been proposed. It is useful to think of primary conversion of wave energy by an oscillating system as a wave-interference phenomenon. Corresponding to optimum wave interference, there is an upper bound to the amount of energy that can be extracted from a wave by means of a particular oscillating system. Taking physical limitations into account, another upper bound, for the ratio of extracted energy to the volume of the immersed oscillating system, has been derived. Finally, the significance of the two different upper bounds is discussed.

Introduction

Impressed by the force of ocean waves, inventors have, for more than two centuries, proposed many different devices for utilising wave power for human purposes [1], [2], [3], [4], [5]. As petroleum became the most important modern source of energy, the interest for wave-energy utilisation faded after the First World War. In the late 1940s, the Japanese wave-power pioneer Yoshio Masuda [6] started to test and develop wave-energy devices. Two inventive European pioneers, Stephen Salter and Kjell Budal, initiated in 1973 wave-power research at universities in Scotland and Norway, respectively. In the US, Michael E. McCormick was an early academic wave-power researcher. In years following the oil crisis in 1973, many researchers at universities and other institutions took up the subject of wave energy. Larger government-funded R&D programmes were started, during the late 1970s, in some European countries, the UK, Sweden and Norway—subsequently also in other countries. During the early 1980s, when the petroleum price declined, wave-energy funding was drastically reduced [7]. A few first-generation prototypes were, nevertheless, tested in the sea. More recently, following the Kyoto protocol on reduction of CO₂ emission to the atmosphere, there is again a growing interest for wave-energy R&D in many countries. As many new young researchers are now entering into this research field, the present paper is intended to convey an overview on knowledge accrued until now, but in particular during years around 1980.

The global power potential represented by waves that hit all coasts worldwide, has been estimated to be in the order of 1 TW (1 terawatt=10¹² W) [8]. If wave energy is harvested on open oceans, energy that is otherwise lost in friction and wave breaking, may be utilised. Then the global wave-power input is estimated to be one order of magnitude larger (∼10¹³ W), a quantity that is comparable with the world's present power consumption. Although this is only a small proportion of the world's wind power potential, which, in turn, is only a small portion of global solar power, ocean waves represent an enormous source of renewable energy. As solar energy is converted to wind energy, the time-averaged power flow is spatially concentrated, from an intensity of typically 0.1–0.3 kW/m² horizontal surface of the earth to 0.5 kW/m² envisaged area perpendicular to wind direction. As wind energy is converted to wave energy, even more spatial concentration takes place. Just below the ocean surface, average power flow intensity is typically 2–3 kW/m² of envisaged area perpendicular to direction of wave propagation. This increase in power intensity, and also the fact that wave energy is more persistent than wind energy, stimulate motivation and hope for developing the, still rather undeveloped, wave-power technology to a prosperous mature level in the future. If the technology can be successfully developed, the market potential is enormous.

In the present paper, the main subject of the next section is the energy associated with ocean waves. Then follow, first, a section on fundamental principles for absorption of wave energy and on various ways of classifying wave-energy converters into different categories, and secondly, a section on mathematical description of wave-energy extraction. Before the final section with concluding remarks, there is a section, where upper bounds to the extracted wave energy are discussed.