Triangular temporal-distribution law for disintegrating internal solitons over a step

Internal solitary waves have been found to disintegrate into a series of solitons over variable bathymetry, with important applications for offshore engineering. Considering realistic background stratification in the South China Sea, internal solitary waves propagating over a step are studied here. By assuming disintegrated solitons propagate independently, a theoretical model, namely a triangular temporal-distribution law based on the Korteweg-de Vries theory, is proposed to describe the fission process of internal solitary waves undergoing disintegration. A parameter is then introduced to quantify the accuracy of the theoretical model. The results indicate that the triangular law predicts the fission process better for a longer travelling distance and a larger amplitude of internal solitary waves.