Wave Period Ratios and the Calculation of Wave Power

An informed, and accurate, characterization of the wave energy resource is an essential aspect selection of suitable sites for the first commercial installations of wave energy converters. This paper describes a detailed study on the variability of wave climate and measured spectral shapes and how they differ from the standard formulations prescribed by theory. In particular dissonance between the ratio of the energy period (TE) to the average zero-crossing period (T02) is investigated at a range of open ocean locations. This relationship is important in the context of resource assessment as many previous works, lacking in detailed spectral data, have often assumed an incorrect ratio. This in turn has influenced the accuracy of the resulting estimates of wave energy. It is demonstrated that the earlier use of the frequently-employed wave period ratios is erroneous and more suitable relationships are presented for the Bretschneider and JONSWAP theoretical spectra. Furthermore, analysis of measured buoy data from real sea-states is used to illustrate that this relationship can in fact vary significantly in practice, depending on geographical location and the prevalent wave conditions. The variability that exists in spectral shape and bandwidth, and the effect this has on the relationship between TE and T02, is illustrated through the comparison of recorded spectra with the Bretschneider spectrum. Analysis of a fifteen year dataset measured by a buoy off the coast of Southern California is presented to illustrate how the wave period ratio fluctuates on a seasonal and interannual basis, while it is also shown that previous studies of the Irish wave energy resource may have underestimated the theoretical power available by as much as 18%. INTRODUCTION Characterizing the wave energy resource in locations where there is a scarcity of quality wave measurements particularly spectral data necessitates the need for assumptions based on theory to be made in order to infer some of the required parameters. For example, the Irish MBuoy network managed by the Marine Institute provides values for the average zero-crossing period (Tz or T02) but in the context of wave energy resource assessment parameters such as the peak period (Tp), the energy period (TE), and increasingly the mean period (T01) are used more frequently. Wave models may suffer from similar shortcomings if their outputs are constrained to a reduced range of parameters in an effort to decrease computation time. For regular sea states, in deep water, the power per unit width of wave crest, P, is given by Equation 1, where Hm0 is the significant wave height. P = 0.49Hm0 2 TE (1) In order to determine the necessary TE values from limited datasets it has been common practice to employ fixed conversion factors based on a theoretical spectral shape, such as Bretschneider or JONSWAP, which is deemed to be representative of the dominant local wave conditions. As a result, assessments of wave energy resource which rely on this approach are sensitive to inaccuracies if the incorrect relationship between parameters is assumed or if the spectral shape considered characteristic for the data is inappropriate. An illustration of how an unsuitable assumption can result in imprecision in the calculation of the available wave power is contained in the Accessible Wave Energy Resource Atlas [1], the standard reference for Ireland’s potential resource. In this study the theoretical