On the application of Miyata-Choi-Camassa model to surface waves

The strongly nonlinear Miyata-Choi-Camassa model, a two-layer internal-wave model that includes the free-surface effect (MCC-FS model), has shown excellent performance on simulating large-amplitude internal waves. In this study, we are interested in assessing whether the MCC-FS model can be applied to study problems involving surface waves, and how the model performs. For this purpose, we apply the two-layer MCC-FS model to a time-varying bottom to simulate surface water-waves by setting the same densities of the upper- and lower-fluid layers. Although densities of the upper and lower fluid layers are the same, it is found that the depth ratio of the two layers plays a remarkable role in the solution. By analyzing the linear dispersion relations of the MCC-FS model with three different depth ratios ( \(\varvec{h}_{\varvec{1}}/\varvec{h}_{\varvec{2}}=\varvec{1}/\varvec{9}\) ${\mathit{h}}_{\mathbf{1}}/{\mathit{h}}_{\mathbf{2}}=\mathbf{1}/\mathbf{9}$ , \(\varvec{3}/\varvec{7}\) $\mathbf{3}/\mathbf{7}$ and \(\varvec{5}/\varvec{5}\) $\mathbf{5}/\mathbf{5}$ , where \(\varvec{h}_{\varvec{1}}\) ${\mathit{h}}_{\mathbf{1}}$ and \(\varvec{h}_{\varvec{2}}\) ${\mathit{h}}_{\mathbf{2}}$ are the depths of the upper- and lower-fluid layers, respectively), we determine that the MCC-FS model with the depth ratio \(\varvec{3}/\varvec{7}\) $\mathbf{3}/\mathbf{7}$ has the better performance on simulating surface water-waves. Under this configuration, we apply the MCC-FS model to simulate the surface solitary waves on a flat bottom, the solitary wave propagating over a submerged shelf and the surface water-waves generated by a bottom disturbance. By comparing with the laboratory measurements, the accuracy of the results provided by the MCC-FS model is validated.