Broadband absorption of ocean wave energy using a graded array of heaving buoys in three dimensions

The generation of renewable power from ocean waves at a commercial scale requires arrays of wave energy converters (WECs) to be designed for efficient power capture over broad frequency bands and a wide range of incident wave directions. Here, array designs are developed in a three-dimensional model based on linear potential-flow theory, by arranging heaving-buoy-type WECs into rows, and spatially grading the resonant properties of successive rows via linear spring–damper power take-off (PTO) mechanisms. The grading leverages theories for rainbow reflection and rainbow absorption, and involves analyses of Bloch waves and pole–zero pairs in complex frequency space to inform the array layout and choice of PTO parameters. The spacing within an array alters the resonant properties of the rows and the behaviour of higher-order passbands, which has implications for the efficiency of an array. Strategies are developed to grade arrays composed of rows with infinitely many WECs, for efficient, broadband absorption over a broad target frequency range, and average absorptions exceeding 90 percent sign 90 % $90\\,\\%$ are achieved over a wide range of wave directions. The strategies are applied to finite arrays, which demonstrate broadband absorption in directionally spread irregular sea states, and are shown to outperform the absorption of uniform arrays across a wide range of peak periods.