On the application of circular–cylindrical waves to ocean wave power absorption

This study derives mathematical forms for the waves radiated from a heaving, surging and swaying point source on the surface of a three dimensional ocean. The interactions between a monochromatic plane wave and monochromatic circular–cylindrical radiated waves are examined, and solutions to the time averaged power are calculated. These calculations confirm pre-existing theoretical maximum absorption lengths for both a heaving and surging point source. The derivations also lead to the definition of the amplitude, phase and form of the radiated waves required to achieve these maximums.Two experimental case studies match measured radiated wave with circular waves. These matches demonstrate a correlation between the body motions and the dominant form of radiated waves as well as higher frequency waves.The study develops three general guidelines for the design of efficient point absorber wave energy converters (PAWECs). Optimum power absorption occurs when the PAWEC radiates theoretical heave and surge waves of the appropriate amplitude and phase. Theoretical sway type waves should be minimized as these radiate energy and do not interact with the incident wave. Similarly, the radiation of higher harmonic waves should also be minimized for the same reasons.

► Circular waves are defined as circular–cylindrical Laplace equation solutions.
► Circular waves are related to waves radiated by a body undergoing different motions.
► Radiated power and group velocity for circular waves are calculated.
► Circular waves and plane waves are combined, and absorbed power is calculated.
► Experimental data from heave and surge tests are compared to the mathematical forms.