Comparison of time-dependent extended mild-slope equations for random waves

The extended mild-slope equations of Suh et a]. [Suh, K.D., Lee, C., Park, W.S., 1997. Time-dependent equations for wave propagation oil rapidly varying topography. Coastal Eng., 32, 91 - 117] and Lee et al. [Lee, C., Kim, G., Suh, K.D., 2003. Extended mild-slope equation for random waves. Coastal Eng., 48, 277-287] are compared analytically and numerically to determine their applicability to random wave transformation. The geometric optics approach is used to compare the two models analytically. In the model of Suh et al., the wave number of the component wave with a local angular frequency omega is approximated with an accuracy of O(omega - (omega) over bar) at a constant water depth, where (omega) over bar is the carrier frequency of random waves. In the model of Sub et al., however, the diffraction effects and higher-order bottom effects are considered only for monochromatic waves, and the shoaling coefficient of random waves is not accurately approximated. This inaccuracy arises because the model of Sub et al. was derived for regular waves. In the model of Lee et al., all the parameters of random waves such as wave number, shoaling coefficient, diffraction effects, and higher-order bottom effects are approximated with an accuracy of O(omega - (omega) over bar). This approximation is because the model of Lee et al. was developed using the Taylor series expansion technique for random waves. The result of dispersion relation analysis suggests the use of the peak and weighted-average frequencies as a carrier frequency for Suh et al. and Lee et al. models, respectively. All the analytical results are verified by numerical experiments of shoaling of random waves over a slightly inclined bed and diffraction of random waves through a breakwater gap on a flat bottom. (C) 2005 Elsevier B.V. All rights reserved.