Numerical investigation of the propagation of internal solitary waves and their reflection by a vertical wall based on a fully nonlinear model

Propagation of internal solitary waves (ISWs) influenced by typical structures have garnered significant attention. We investigate the propagation of ISWs and their reflection by a vertical wall using multi-domain boundary element method (MDBEM). Fully nonlinear boundary conditions at the interface and free surface conditions at the top surface are considered in the simulations. Meanwhile, laboratory experiments are conducted to validate the constructed numerical model. Wave profiles, resident time, and flow fields for different initial amplitudes and density ratios are calculated and analyzed. Wave amplitudes significantly influence the nonlinear component of wave phase speed. The ratio between the nonlinear speed and the total velocity is only $4.5\%$ for $a/h_1=0.1$, but this value can reach $32\%$ for $a/h_1=0.1$. The resident time of an ISW attaching to the vertical wall decreases with the increasing initial wave amplitude and reaches a constant value for waves with amplitudes larger than $a/h_1=0.6$. Particle velocity in the upper layer is opposite to that in the lower layer, and the vertical velocity becomes dominant as the wave approaches the wall. Surface displacement, presented as a surface solitary wave with an opposite phase induced by an ISW, is obtained and discussed through the numerical model.