A note on extension of fully dispersive weakly nonlinear wave equations for rapidly varying topography

Abstract

Following the approach proposed by Nadaoka et al. [Nadaoka, K., Beji, S. and Nakagawa, Y. (1997) A fully dispersive weakly nonlinear model for water waves, Proc. Roy. Soc. London A453, pp. 303-318], we present a set of one-dimensional weakly nonlinear single-component wave equations for rapidly varying topography by including the bottom curvature and squared bottom slope terms ignored in the original equations of Nadaoka et al. To solve the linear version of the extended wave equations derived in this study, a finite difference numerical model is constructed. The performance of the model is tested for the case of wave reflection from a plane slope and a rippled bed. Numerical results are compared with those calculated using other numerical models reported earlier. It is shown that the accuracy of the present numerical model is improved significantly in comparison with that of the original equations of Nadaoka et al. by including a complete set of higher order bottom effect terms for a rapidly varying topography.