Experimental and numerical studies on internal solitary waves with a free surface

Large-amplitude internal solitary waves in a two-layer fluid system with a free surface are investigated in this paper. Laboratory experiments on strongly nonlinear internal solitary waves with a free surface for a deep configuration are conducted. After comparing the experimental data with the results of the Miyata–Choi–Camassa model that includes the free-surface effects (MCC-FS), we find that the MCC-FS model does not calculate accurately the internal solitary waves with a free surface. Thus, we develop a strongly nonlinear model for a deep configuration, namely the two-layer high-level Green–Naghdi (HLGN-FS) model that includes the free-surface effects. Numerical results of the HLGN-FS model, including the wave profile, velocity field and wave speed, are presented for three cases. The first case is a shallow configuration with ρ2/ρ1 = 0.977 and h2/h1 = 1/4.13, where ρ2 and ρ1 are the densities of the upper-fluid layer and the lower-fluid layer, respectively, and h2 and h1 are the depths of the upper-fluid layer and the lower-fluid layer, respectively. The second case is also a shallow configuration, where h2/h1 = 1/5 while ρ2/ρ1 = 0.859. The third case is related to the present physical experiments, where ρ2/ρ1 = 0.869 and h2/h1 = 1/15. It is shown that the MCC-FS model can provide accurate results for the shallow configurations. Meanwhile, the HLGN-FS model is shown to be accurate for describing the internal solitary waves for both shallow and deep configurations.