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The various patterns of internal solitary wave interactions are complexphenomena in the ocean, susceptible to the influence of shear flow and densitydistributions. Satellite imagery serves as an effective tool for investigatingthese interactions, but usually does not provide information on the structureof internal waves and their associated dynamics. Considering a three-layerconfiguration that approximates ocean stratification, we analyticallyinvestigate two-dimensional internal solitary waves (ISW) in a three-layerfluid with shear flow and continuous density distribution using the(2+1)-dimensional Kadomtsev-Petviashvili (KP) model. Firstly, the KP equationis derived from the basic governing equations which include mass and momentumconservations, along with free surface boundary conditions. The coefficients ofthe KP equation are determined by the vertical distribution of fluid density,shear flow, and layer depth. Secondly, it is found that the interactions of ISWcan be carefully classified into five types: ordinary interactions includingO-type, asymmetric interactions including P-type, TP-type and TO-type, andMiles resonance. The genuine existence of these interaction types is observedfrom satellite images in the Andaman Sea, the Malacca Strait, and the coast ofWashington state. Finally, the ``bright" and ``dark" internal solitaryinteractions are discovered in the three-layer fluid, which together constitutethe fluctuating forms of oceanic ISW. It is revealed that shear flow is theprimary factor to determine whether these types of interactions are ``bright"or ``dark". Besides, a detailed analysis is conducted to show how the ratio ofdensities influences the properties of these interactions, such as amplitude,angle, and wave width.

Oceanic internal solitary wave interactions via the KP equation in a three-layer fluid with shear flow