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

Wave Reflection from Nearshore Depressions

“…These errors in the MSE solution are primarily due to the bottom curvature induced by the slope discontinuity at both ends of the transitional slope. Lee et al (1998) found the mild-slope approximation to be even more limiting when waves of a range of relative water depths kh were considered. Finally, Kirby and Misra (unpublished manuscript) argued that the MSE is not the correct leading-order approximation even for a slowly varying sea bed.…”

“…For practical applications, where our interest is ultimately in the shoreline response to the presence of localized bottom features, it is also necessary to choose a model that can handle non-idealized bathymetries. For these reasons, we have chosen the finite difference formulation of the MMSE as given by Lee et al (1998). Since this model solves the equations in hyperbolic form, it also has the advantage of requiring shorter computational times as compared to models using the elliptical form.…”

“…(1) and (2) reduce to the MSE model of Copeland (1985). In their numerical implementation, Lee et al (1998) uses a conservative grid size to wavelength ratio of 60 to guarantee satisfactory spatial resolution.…”

“…{C g /C -R 1 (h) 2 -R 2  2 h} ≤ 0), which tends to occur at sharp transitions in depth where the curvature is large. As an empirical fix, Lee et al (1998) recommend altering the curvature and slope squared terms locally by selecting the smallest possible integer j necessary to keep the denominator term in Eq.…”

“…The MMSE formulation of Lee et al (1998) constitutes a hyperbolic system of first-order equations here given by…”