Nejadkazem, O. and Gharabaghi, A.R.M., 2012. Mathematical model for hydrodynamic behavior of an array of vertical cylindrical piles used as a breakwater. Journal of Coastal Research, 28(6), 1446–1461. Coconut Creek (Florida), ISSN 0749-0208.

A mathematical model is developed to study hydrodynamic behavior of an array of vertical cylindrical piles used as a breakwater (VPB) under irregular waves that impinge normally. The numerical calculation is based on an eigenfunction method and utilizes matched asymptotic boundary conditions. The concept of energy spectra has been used for modeling real hydrodynamic sea wave characteristics, and evanescent modes were considered for each wave component. A new empirical formula for estimation of the contraction coefficient is proposed that includes hydrodynamic wave characteristics in addition to the geometry of a breakwater. The formula models effects of both vena contracta and nonpropagating waves and is advantageous from the prospect of effectiveness and efficiency. Consequently, few evanescent terms are necessary for the eigenfunction expansion method to be confident about the accuracy of results. Results are given for reflection, transmission, and dissipation, and the theoretical value was found to agree quite well with experimental data available in literature. It is concluded that an efficient range of porosity may be located in [0.1, 0.2], and the steeper wave reflects more and transmits less. Also, in shallow and intermediate water depth, the VPB operates optimally and dissipates the energy of waves effectively. The VPB is recommended for significant wave periods of more than 2.0 seconds and performs better for a wave steepness of less than 0.025.