Construction of a wavefront model for internal solitary waves and its application in the Northern South China Sea

Internal solitary waves (ISWs) play a crucial role in the development of various physical and biological processes, and numerous high-precision two-dimensional or three-dimensional numerical models have been developed to simulate the generation and propagation processes of ISWs. However, these numerical models, especially when simulating the interaction between ISWs and ocean circulation, require substantial computational resources. This burden can make it challenging to apply them in real-time or short-term forecasting scenarios. In this study, we propose a new numerical model for ISWs by combining traditional one-dimensional ISW theory with wave refraction theory. The proposed model resolves the issues of ray crossing and divergence, which are commonly encountered in traditional refraction models, by employing equally spaced grids along the wave crest line. As a result, this model is capable of simulating the far-field propagation of ISWs. This model enables rapid prediction of the vertical structure and wave crest morphology of ISWs in specific current fields and at given time frames, and it is utilized to investigate the characteristics and propagation of ISWs generated by the nonlinear steepening of internal tide (IT) in the South China Sea. Comparative analysis with satellite imagery demonstrates the model's accurate representation of ISW processes and phenomena, such as wave crest line discontinuities, diffraction, and wave‒wave interactions when passing through Dongsha Island. Furthermore, propagation time estimates based on this model have errors of ±0.98 h (1σ) over which the ISWs are observed by a mooring system, and the average time difference is 0.81 h.