Kieran Umit Monk, Qingping Zou, Daniel Conley


A computationally efficient approximate analytical solution based on the classic solution for diffraction about a semi-infinite breakwater, is developed to assess the wave energy shadow down-wave of a single row array of overtopping type wave energy converters approximated as partially transmitting breakwater segments. The approximations associated with the solution are mitigated by a comparison with the mathematically exact but more computationally expensive boundary element method for the same problem. The approximate analytical solution is compared with a non-physical solution where diffraction is not accounted for to quantify the net re-distribution of wave energy by the diffraction mechanism with increasing down-wave distance from the array.


wave energy converter; wave energy shadow; scattering; diffraction; breakwater, wave dragon;

Full Text:



Beels, C., Troch, P., De Visch, K., Kofoed, J.P. and De Backer, G., 2010. Application of the time-dependent mild-slope equations for the simulation of wake effects in the lee of a farm of wave dragon wave energy converters. Renewable Energy, 35(8), 1644-1661.

Black, K., 2007. Review of wave hub technical studies: Impact on inshore surfing beaches. ASR ltd.

Daemrich, K.-F. and Kohlhase, S., 1978. Influence of breakwater reflection on diffraction. Proceedings of the 16th International Conference on Coastal Engineering. ASCE, 651-663

Hotta, S., 1978. Wave height distribution around permeable breakwaters. Proceedings of the 16 th International Conference on Coastal Engineering. ASCE, 695-714

Kim, S.D. and Lee, H.J., 2010. The comparison of analytical and numerical solutions for wave diffraction due to insular breakwater. International Journal of Physical Sciences, 5(3), 226-237.

McCormick, M.E. and Kraemer, D.R.B., 2002. Polynomial approximations for fresnel integrals in diffraction analysis. Coastal Engineering, 44(3), 261-266.

Millar, D.L. Smith, H.C.M. and Reeve, D.E., 2007. Modelling analysis of the sensitivity of shoreline change to a wave farm. Ocean Engineering, 34(5-6), 884-901.

Mitsui, H. and Murakami, H., 1967. Wellenhöhenverteilung an diskontinuierlichen teilen von kustenbauwerken. Kaigan Kogagu Koenkai Koenshu 14

Monk, K. Zou, Q. Conley, D. 2012a. An approximate solution for the wave energy shadow in the lee of an array of overtopping type wave energy converters. Costal engineering. under review

Monk, K.U., Zou, Q.-P., and D. C. Conley 2012b. Numerical and Analytical Simulations of Wave Interference about a Single Row Array of Wave Energy Converters, Estuary and Coast, submitted.

Nørgaard, J. H. and Andersen, T. L., 2012. Investigation of Wave Transmission from a Floating Wave Dragon Wave Energy Converter, Proceedings of the 22 nd International Offshore and Polar Engineering Conference, 509-516.

Ou, Shan-Hwei., Tzang. Shiaw-Yih., Hsu. Tai-Wen., 1988. Wave field behind the permeable detached breakwater, Proceedings of the 21 st International Conference on Coastal Engineering.

Penney, W.G. and Price, A.T., 1952. The diffraction theory of sea waves and the shelter afforded by breakwaters. Phil. Trans. R. Soc, (Ser. A 244), 236-253.

Silvester, R. and Lim, T.-K., 1968. Application of wave diffraction data. Proceedings of the 11th International Conference of Coastal Engineering, ASCE, 248-270

Sommerfeld, A., 1886. Mathematische theorie der diffraction. Math Annalen, 47, 317-374.

Venugopal, V. and Smith, G.H., 2007. Wave climate investigation for an array of wave power devices. 7th European wave and tidal energy conference.

Yu, X. and Togashi, H. 1996. Combined diffraction and transmission of water waves a around porous breakwater gap. Proceedings of the 25th International Conference of Coastal Engineering. ASCE, 2063-2076