Abstract
A higher-order mild-slope equation (HOMSE) is derived based on theory of Hsu et al. [14]. Depth function is approximated up to third-order accurate in terms of both wave nonlinearity and bottom slope. Classical Galerkin method is used to solve HOMSE. Developed model is verified with a series of benchmark tests, including propagation of a sinusoidal wave past a submerged bar, wave propagating on a sloping bed, wave propagating over an elliptic shoal on a uniform slope, and wave propagating through a semicircular slope bottom, respectively. Computed results are compared with experiment data and prediction of low-order mild-slope equation model as well as Boussinesq equations model, and show good agreement.
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