Hyperbolic mild-slope equations extended to account for rapidly varying topography

Abstract

In this paper, following the procedure outlined by Copeland [Copeland, G.J.M., 1985. A practical alternative to the mild-slope wave equation. Coastal Eng. 9, 125-149.] the elliptic extended refraction-diffraction equation of Massel [Massel, S.R., 1993. Extended refraction-diffraction equation for surface waves. Coastal Eng. 19, 97-126.] is recasted into the form of a pair of first-order equations, which constitute a hyperbolic system. The resultant model, which includes higher-order bottom effect terms proportional to the square of bottom slope and to the bottom curvature, is merely an extension of the Copeland's model to account for a rapidly varying topography. The importance of the higher-order bottom effect terms is examined in terms of relative water depth. The model developed is verified against other numerical or experimental results related to wave reflection from a plane slope with different inclination, from a patch of periodic ripples, and from an are-shaped bar with different front angle. The relative importance of the higher-order bottom effect terms is also examined for these problems. (C) 1998 Elsevier Science B.V. All rights reserved.