A parabolic equation extended to account for rapidly varying topography

In this paper, following the procedure outlined by Li (1994. An evolution e quation for water waves. Coastal Engineering, 23, 227-242) and Hsu and Wen (2000. A study of using parabolic model to describe wave breaking and wide- angle wave incidence. Journal of the Chinese Institute of Engineers, 23(4), 515-527) the extended refraction-diffraction equation is recasted into a t ime-dependent parabolic equation. This model, which includes higher-order b ottom effect terms, is extended to account for a rapidly varying topography and wave energy dissipation in the surf zone. The importance of the higher -order bottom effect terms is examined in terms of the relative water depth . The present model was tested for wave reflection in a number of different environments, namely from a plane slope with different inclinations, from a patch of periodic ripples. The model was also tested for wave height dist ribution around a circular shoal and wave breaking on a barred beach. The c omparison of predictions with other numerical models and experimental data show that the validity of the present model for describing wave propagation over a rapidly varying seabed is satisfactory. (C) 2001 Elsevier Science L td. All rights reserved.