Suastika, K., 2012. Nonlinear-dispersion effects in modeling of blocking of Stokes waves.
Effects of amplitude dispersion are investigated in modeling of blocking of Stokes waves in deep water. Modeling results of the wave-amplitude evolution using, respectively, the linear- and Stokes third-order dispersion relation, are compared with experimental data. Two data sets with relatively small-wave steepness are considered because of model restriction to weakly-nonlinear waves. The wave period in Test 1 is 1.1 s and in Test 2 is 1.2 s. The initial-target wave amplitude in still water in Test 1 is 1.0 cm, which is the same as Test 2. It is found that inclusion of amplitude dispersion in the model results in a larger wave-group velocity, as expected, and gives a better fit to the experimental data as compared to the use of the linear-dispersion relation. More specifically, using the Stokes third-order dispersion relation instead of the linear-dispersion relation in the model, the root-mean-squared error ξ, used as a measure for the goodness-of-fit between the experimental data and model-results, decreases from 3.5 × 10−3 to 1.8 × 10−3 in Test 1 and from 3.4 × 10−3 to 2.4 × 10−3 in Test 2.
