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SUMMARYIn order to understand the nonlinear effect in a two-layer system, fully nonlinear strongly dispersive internal-wave equations, based on a variational principle, were proposed in this study. A simple iteration method was used to solve the internal-wave equations in order to solve the equations stably. The applicability of the proposed numerical computation scheme was confirmed to agree with linear dispersion relation theoretically obtained from variational principle. The proposed computational scheme was also shown to reproduce internal waves including higher-order nonlinear effect from the analysis of internal solitary waves in a two-layer system. Furthermore, for the second-order numerical analysis, the balance of nonlinearity and dispersion was found to be similar to the balance assumed in the KdV theory and the Boussinesq-type equations.

[1] Residual currents due to internal wave breaking on a uniform slope were investigated in a two-layer system using laboratory experiments and numerical computations for different layer configurations. Internal wave-induced currents over a slope were measured in an experimental tank using PIV and also reproduced by a hydrodynamic model to quantify the detailed velocity field. The present results reveal that the critical level derived from the KdV theorem is a useful parameter for classifying the dynamics of internal waves breaking over a slope. As the horizontal distance from the critical level point to the internal wave breaking point increases, internal waves break more dynamically over the slope. Consequently, residual currents are enhanced near the breaking point. These findings increase our capacity to understand flux paths of biological and chemical substances in the stratified coastal ocean.Citation: Nakayama, K., T. Shintani, K. Kokubo, T. Kakinuma, Y. Maruya, K. Komai, and T. Okada (2012), Residual currents over a uniform slope due to breaking of internal waves in a two-layer system,

The oblique reflection of an incident internal solitary wave is investigated using a fully-nonlinear and strongly-dispersive internal wave model. The 3 rd order theoretical solution for an internal solitary wave in a two-layer system is used for the incident solitary wave. Two different incident wave amplitude cases are investigated, in which nine and eleven different incident angles are used for the small and large incident amplitude cases respectively. Under both amplitudes, at least for the cases investigated here, relatively smaller incident angles result in Mach reflection while relatively larger incident angles result in regular reflection. Under Mach-like reflection generation of a 'stem' is observed for a certain range of incident angles, in addition to the reflected wave. The stem is found to have, in a certain sense, the characteristics of an internal solitary wave, though the maximum stem wave amplitude is less than four times as large as the original incident internal solitary wave. The stem length is confirmed to increase faster for the larger incident wave amplitude.The maximum amplification factor for the small incident wave is the same as in previous studies.However, the maximum amplification factor for the large incident wave is less than that for the small wave. The results of these calculations are compared with those of the corresponding KP theory and it is found that a lower amplification factor may be a significant characteristic of internal solitary waves.