The effect of top surface boundary conditions on internal solitary waves in numerical simulations

Numerical simulations of internal solitary wave (ISW) propagation are extensively employed to assess their impact on marine structures and ecosystems. In such simulations, rigid-lid and free-surface boundary conditions are commonly implemented at the top computational boundary. While the rigid-lid condition simplifies model setup and reduces computational cost by fixing the upper surface, the free-surface condition more accurately represents ocean surface physics. This study quantitatively evaluates the influence of these surface boundary conditions on ISW dynamics using a fully nonlinear numerical model. Comparative simulations are conducted across varying density differences, initial wave amplitudes, and depth ratios. Results reveal that under large density differences, the choice of boundary condition (rigid-lid vs free-surface) significantly alters ISW wave profiles, phase speeds, and flow fields. However, for a small density difference close to the real ocean (e.g., ρ1/ρ2=1000/1025), both conditions yield indistinguishable results across key ISW characteristics. Furthermore, under these realistic density differences, the effects of top boundary conditions remain negligible regardless of variations in initial wave amplitude or depth ratio. Consequently, for oceanographically relevant scenarios, the rigid-lid condition achieves comparable accuracy to the free-surface condition in predicting ISW characteristics. This supports its utility in simplifying ISW propagation and evolution simulations when surface wave interactions are not of primary interest. Additionally, the Miyata–Choi–Camassa theory solution proves suitable as an initial wave profile condition, applicable for both small and large wave amplitudes.