The role of the free surface on interfacial solitary waves

Abstract

We investigated theoretically and experimentally internal solitary waves (ISWs) in a twolayer fluid system with a top free surface. Laboratory experiments are performed by lockrelease, under Boussinesq and non-Boussinesq conditions. Experimental results are compared with those obtained by the analytical solution of Korteweg-de Vries (KdV) weakly nonlinear equation, and by the strongly nonlinear Miyata-Choi-Camassa (MCC) model. We analyze the initial conditions which allow to find soliton solutions for both rigid-lid (-RL) and free-surface (-FS) boundary conditions. For the MCC-FS model, we employ a new mathematical procedure to derive the ISW-induced free surface displacement. The density structure strongly affects the elevation of the free surface predicted by the MCC-FS model. The free surface maximum displacement increases mostly with the density difference, assuming non-negligible values also for smaller interfacial amplitudes. Larger displacements occur for thinner upper layer thickness. The MCC-FS model gives the best prediction in terms of both internal waves geometric/kinematic features and surface displacements. The exsistence of a free surface allows the ISW to transfer part of its energy to the free surface: the wave celerity assumes lower values with respect to ISW speed resulting from the MCC-RL model. For ISWs with a very large amplitude, this behavior tends to fade, and the MCC-RL and the MCC-FS model predict approximately the same celerity and interfacial geometric features. For small-amplitude waves, also predictions of the KdV-RL equation are consistent with experimental results. Thus, ISWs with an intermediate amplitude should be modeled taking into account a free top surface as boundary condition.

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

“…Meanwhile, for this deep-configuration case, we find that the surface-wave profiles obtained by the MCC-FS model are obviously higher and wider than those obtained by the HLGN-FS model. Similar to La Forgia & Sciortino (2019), we measured the maximum surface elevation of the top-fluid layer recorded in the laboratory experiments as shown in figure 20. Good agreement is found between the numerical results and the experimental data.…”

“…higher and wider than these obtained by the HLGN-FS model. Meanwhile, similar to Forgia & Sciotino (2019), we measured the maximum surface elevation of the top fluid layer recorded in the laboratory experiments as shown in Figure 20. Good agreement is found between the numerical results and the experimental data.…”

“…They showed that the wave profiles obtained by the MCC-RL model were wider and the wave speeds were larger than the results obtained by the MCC-FS model. La Forgia & Sciortino (2019) conducted experiments on internal solitary waves with a free surface and measured the maximum surface elevation right above the trough of the internal solitary wave. They showed that the maximum surface elevation increased (with respect to the upper-layer depth) with smaller density ratio , and smaller depth ratio .…”

Mixing Efficiency for Breaking Internal Solitary Waves

“…Indeed, in the coastal ocean, the typical value of the Boussinesq parameter, that is, the ratio of the density difference between the two layers and a reference density, is about 0.03 (Chen et al, 2007). We observe that, for this value, the effects of the disturbances at the free surface are negligible, and do not have significant impact on the induced mixing (Kodaira et al, 2016;la Forgia & Sciortino, 2019). The different depths of the pycnoclines of the two stratifications produces the interfacial displacement η P ; a sloping boundary, making an angle θ with the horizontal, is placed on the right hand-side of the tank to induce the ISWs breaking and partial reflection (Figure 2).…”

Breaking Location of Internal Solitary Waves Over a Sloping Seabed

“…Indeed, for ISWs propagating in stratified ambient fluids with small density differences (as those usually observed in the ocean), the free surface displacements are negligible when compared with the subsurface ones. In particular, to an internal displacement of 50 m, a surface displacement of about 4 cm is predicted by the MCC–FS (Free‐Surface) model (Kodaira et al., 2016; La Forgia & Sciortino, 2019). Thus, we can replace the free surface with a rigid boundary.…”