Numerical studies of internal solitary wave generation and evolution by gravity collapse

Abstract

In this study, an analysis on the internal wave generation via the gravity collapse mechanism is carried out based on the theoretical formulation and the numerical simulation. With the linear theoretical model, a rectangle shape wave is generated and propagates back and forth in the domain, while a two-dimensional non-hydrostatic numerical model could reproduce all the observed phenomena in the laboratory experiments conducted by Chen et al. (2007), and the related process realistically. The model results further provide more quantitative information in the whole domain, thus allowing an in depth understanding of the corresponding internal solitary wave generation and propagation. It is shown that the initial type of the internal wave is determined by the relative height between the perturbation and the environmental density interface, while the final wave type is related to the relative height of the upper and lower layers of the environmental fluid. The shape of the internal wave generated is consistent with that predicted by the KdV and EKdV theories if its amplitude is small, as the amplitude becomes larger, the performance of the EKdV becomes better after the wave adjusts itself to the ambient stratification and reaches an equilibrium state between the nonlinear and dispersion effects. The evolution of the mechanical energy is also analyzed.