Development of the parabolic equation for calculation of sea waves diffraction in port area

Abstract

   Application method of parabolic equations is presented in this paper for calculating diffraction of sea waves behind converging breakwaters, which entrance is not parallel to front of approaching waves. For this, the method of linear superposition of results obtained separately for each breakwater was used. Based on a comparison of results obtained by this method with results of physical (obtained in a wave basin) and numerical (obtained using DHI MIKE 21 BW) model experiments with different settings (40 models in total), a conclusion about using allowability of the obtained equations was made. Results of the study make it possible to recommend the obtained equations for practical use in studies of seaports wave regimes, where diffraction phenomena are strong. Complexity of a function used in the parabolic method causes appearance of “petals” of diffraction coefficient isolines in protected water area. Approximate equations are presented for smoothing the oscillations of the complex amplitude function along lines parallel and perpendicular to axis of breakwaters. It is shown that associated error in obtaining diffraction coefficient varies on average within 2–5 %, and maximum error obtained was 12.5 %.